00:00Hello, I'm Diego from revision
00:02dojo and welcome to this
00:03new video series on the
00:05IAB Physics 2025 syllabus. Today
00:07we're going to be looking
00:09at 8 .1 .1 describing
00:11motion. It is essentially a
00:13toolbox of different physics concepts
00:16and tools that we can
00:17use to describe and analyze
00:19motion in different dimensions. Today
00:22we're going to look at
00:23vectors and scalars, speed and
00:25velocity, graphing motion, and some
00:27things to leverage
00:28and sub -at equations. Let's
00:30get started. Firstly, let's take
00:32a look at the learning
00:33objectives of A .1 .1.
00:35I highly recommend you write
00:37these down and as we
00:38go through the lesson, you
00:40highlight the concepts that you
00:41need a little bit more
00:42work with and you take
00:43those that you are confident
00:45in understanding. These are the
00:47formulas for A .1 .1
00:49.1. As you can see,
00:49they make up the entirety
00:51of the section of the
00:52formula booklet on A .1.
00:54kinematics. These four formulas
00:56are the stupid equations that
00:57we will be seeing at
00:58the end of this lesson.
01:00So the first section of
01:02this subunit is vectors and
01:04scalars. What we need to
01:06understand at first is that
01:07when we talk about vectors
01:08and scalars, we are talking
01:10about quantities. We are talking
01:12about types of quantities, actually.
01:14The definition of scalar is
01:16as scalar is a physical
01:17quantity with size, but no
01:21direction. The definition of a
01:23vector
01:24is a vector is a
01:25physical quantity with size and
01:28direction. These definitions were directly
01:33taken from the textbook and
01:35I highly recommend you memorize
01:37them. In physics there is
01:39not that much memorizing but
01:40there are still some key
01:41definitions and terms that you
01:43need to remember. Here something
01:45we might want to define
01:46is the concept physical quantity.
01:48What is a physical quantity?
01:50Well a physical quantity is
01:52actually
01:52just any number you get
01:54in physics. A quantity is
01:55just a number and physical,
01:57well, in the physical world.
01:59In the case of physics,
01:59it's something that represents a
02:01variable in a question. It
02:02can be, for example, 15
02:06utens. Or 200 meters. Or
02:14also five tools. All of
02:18these are physical quantities.
02:20Scaler, as you can see,
02:22has size but no direction.
02:24And here, I would like
02:25to point out that there
02:26is another term for size
02:28that is actually magnitude. If
02:34you do math a cell,
02:36you might have encountered vectors
02:38before, and you might know
02:39size as magnitude. They are
02:42essentially the same thing. They
02:43are both completely correct. But
02:45personally, I prefer magnitude as
02:47it is a little bit
02:48more mathematically correct. So a
02:50scalar has no direction. What
02:52does that exactly mean? Direction
02:54is a concept that is
02:56a little bit tricky to
02:57understand. But with that example,
02:59it should be relatively straightforward.
03:02Let's assume you have an
03:03object here, a box, and
03:05you decide to apply a
03:07force on said box. That
03:10force is going to have
03:11a magnitude. It can be,
03:13for example, as we said
03:15here, 15 new
03:16Then that box is going
03:19to move in what direction
03:21is it going to move?
03:22Well, in the direction of
03:23the force applied. And this
03:26is the important thing here.
03:27If you apply this force,
03:29let's suppose in a different
03:30direction. So for example here,
03:34it might still be 15
03:35newtons, but that force would
03:37make that box move in
03:40a different direction. As you
03:42can see, force is a
03:44vector
03:44quantity because it has a
03:46direction. It is applied in
03:48a certain direction. You can
03:50name the direction, for example,
03:52by saying it's going north,
03:53it's going at a 45
03:55degree angle, it's going left
03:57or right. There's many ways
03:59of defining the direction of
04:00a vector. But in any
04:02ways, a vector quantity always
04:04has a direction. The opposite
04:06is obviously the scalar, which
04:08has absolutely no direction. Here,
04:11take a look at the
04:12quantity
04:12is we wrote down here.
04:14Which ones do you think
04:16are vectors and which ones
04:18are scalars? Of course you
04:20already have an answer right
04:21here, 15 Newton is a
04:24force because Newton is a
04:26unit of force. Therefore it
04:28must be a vector. What
04:29about the other two ones?
04:32Five joules is an energy.
04:37Or it can also be
04:39work.
04:40200 meters is a distance
04:44or displacement. We will see
04:52the difference between distance and
04:54displacement in the next section
04:55of this lesson. However, for
04:58now, take these quantities and
04:59tell me which ones do
05:01you think are vectors? If
05:04you answered displacement, that's right.
05:07Energy and work are
05:08both directionless. For example, you
05:11can say that a certain
05:13object has a certain amount
05:16of kinetic energy, but there
05:17is no direction given to
05:20that energy. Same with work.
05:22You can say an object
05:23is doing work, however you
05:25don't have to specify in
05:26which direction it is doing
05:27the work. The work does
05:29not have a direction. Distance
05:31is similar. Distance, we'll see
05:33a little bit later, is
05:34a measure of the length
05:36of the path
05:36taken. Therefore, because it's a
05:38measure of length, it has
05:40no direction. Displacement, on the
05:42other hand, it's a measure
05:44of a difference in position.
05:46Again, don't worry, we'll be
05:48seeing this in the next
05:48section. But because it's a
05:50difference in position, you need
05:51to state in which direction
05:53that difference is. For example,
05:55if you are at point
05:56A here and you move
05:58to point B, your displacement
06:00was downwards. If you were
06:04At point C, if you're
06:06going to point C, your
06:09displacement is not quite downwards,
06:11it's more at an angle.
06:12All right, as promised, now
06:14let's see the difference between
06:15distance and displacement. They are
06:17a perfect example of a
06:19scalar and a vector quantity.
06:22As I stated before, distance
06:24is a scalar. While displacement
06:27is a vector, despite the
06:32fact
06:33they're both measured in meters.
06:35Again, as stated before, distance
06:37is a measure of the
06:45path taken. This is very
06:49important. It's just a measure
06:50of the path taken. For
06:52example, if you're at point
06:55A and you're going to
06:56point B, but you don't
06:58take quite a straight line
07:01Here, your distance is going
07:05to be relatively big. It
07:07is going to be much
07:08bigger than just a straight
07:10line from A to B.
07:12So keep this in line,
07:13keep this little definition here.
07:16Distance is the measure of
07:18the length of the path
07:19you take. On the other
07:21hand, the spicement, as we
07:22stated before, is a difference.
07:29Displacement is a difference in
07:33position. As you can see,
07:35I used Delta here. In
07:36physics, we use Delta to
07:38state a difference or a
07:39change in something. This is
07:41a very important notation that
07:43I recommend you keep in
07:43mind. So displacement is a
07:46difference or a change in
07:47position. So, in taking the
07:50same example, you have point
07:52A and point B, your
07:54displacement is going to be
07:56the difference
07:57between your position at A
08:00and your position at B.
08:02So it's going to be
08:02a straight line between the
08:05two points. It doesn't matter
08:07what path you take, it
08:08doesn't matter the distance you
08:11cover. This placement is always
08:12in a straight line as
08:13it just takes your initial
08:14and final position and works
08:16out the difference. This is
08:19a great example of a
08:20scalar in a vector that
08:21uses the same unit and
08:23represents similar things. Now,
08:25Let's do a quick exercise.
08:27So here are two tables.
08:29I invite you to copy
08:30them down and write down
08:32all the vector quantities you
08:34can think of and all
08:35the scalar quantities you can
08:36think of. The important part
08:38here is remember vectors have
08:40a direction. I already told
08:41you a couple of them.
08:42So for vectors, we have
08:44forces and we also have
08:49displacement. I'm not going to
08:52write it all down.
08:53Then scalars, we have distance,
08:56of course. And we did
09:03mention energy before. And work.
09:08So, try to think of
09:10different quantities. I can give
09:11you examples like speed and
09:13velocity. They both represent very
09:14similar things with which one
09:15is a vector or a
09:16scalar. Try to think about
09:17that and you'll be ahead
09:18of the next part of
09:19the lesson. Although quantities can
09:20be things like
09:21like temperature or mass or
09:24charge or current any other
09:27quantities like that try to
09:28think of them and write
09:30them down in your vectors
09:31and scalars column. Then check
09:33your answers with your classmates
09:34or your physics teacher or
09:36teacher. This is a very
09:38useful exercise because you do
09:39not want to be going
09:40into a physics paper and
09:42be wondering if a certain
09:44quantity is a vector or
09:45a scalar do you have
09:46to take direction into account?
09:47How does it work? You
09:49do not
09:49want to do that. So
09:50you want to really know
09:51your vectors and scalars pretty
09:53well. Trust me, it can
09:54save you quite a few
09:56marks. Alright, let's take a
09:58look at the second section
09:59of this 8 .1 .1
10:02describing motion subunit. It is
10:04speed and velocity. So speed
10:07and velocity are the scalar
10:10and vector quantities that use
10:13the meters per second unit.
10:16So
10:17meters per second, more commonly
10:21written in physics as meters
10:24per second. These notations are
10:29equivalent mathematically just like however
10:35the preferred one is the
10:37one in the middle right
10:38here meters per second with
10:40the negative power. Keep that
10:43in line for the future.
10:44So if I were to
10:45tell you speed
10:45velocity, try to think about
10:47it, which one do you
10:48think is a scalar, and
10:49which one do you think
10:50is a vector? Depending on
10:54your previous physics knowledge, you
10:55might have absolutely no clue,
10:57or you might already know
10:58that speed is a scalar,
11:00and velocity is the vector.
11:02But let's take a look
11:02at why that matters and
11:04what we use it for.
11:06So the important thing to
11:07keep in mind here is
11:09how they are calculated. So,
11:12for example,
11:13speed is distance over top.
11:23The important part again here
11:25is distance. So speed is
11:28distance over time and velocity
11:30is displacement over time. Of
11:36course, you should be able
11:37to tell already that the
11:39velocity is a vector quantity
11:41because
11:41it comes from displacement, another
11:43vector quantity. And this is
11:45a concept in physics and
11:47ultimately also in math that's
11:48quite important to understand. If
11:50to calculate a certain quantity
11:52you need a vector, then
11:54that final quantity is going
11:56to also be a vector
11:57because it has a direction,
11:59it keeps the direction. A
12:01quick way to understand really
12:02why this matters is to
12:04see that speed, for example,
12:06cannot technically be speaking, be
12:08negative. Let's take
12:09take a look at a
12:10quick example. So let's assume
12:13you consider this direction the
12:16positive direction in terms of
12:18velocity. So that means that
12:20anything moving in the direction
12:22of that arrow is moving
12:23with a positive velocity. Essentially,
12:26it's the forward direction. Now,
12:30if you have a car
12:30moving in that direction, for
12:33example, then it has a
12:35positive velocity. If it's velocity,
12:37there is
12:3810 meters per second in
12:40that direction, then its speed
12:43is also equal to 10
12:45meters per second. However, let's
12:48suppose a car suddenly decides
12:50to stop, and it starts
12:54moving backwards. Then, what do
12:59you think it's the velocity
13:02will be? Well, as I
13:04stated before, the positive
13:06direction is the opposite to
13:08the direction it's currently going
13:09in. So it must be
13:10minus 10 meters per second.
13:15Indeed, that would be right.
13:16However, what is its speed?
13:18If its speed has no
13:19direction. That's right. Just 10
13:23meters per second, just like
13:25it was before. So this
13:26is a quick way to
13:27understand the difference between velocity
13:29and speed. Just speed is
13:31a general measure of how
13:33fast it's going whereas
13:34velocity actually gives you a
13:35little bit more information and
13:37we'll see that that matters
13:38much more a little bit
13:39down the line. So let's
13:42take a look at our
13:42first sample question. A plane
13:44flies over Singapore at 720
13:46and over Hong Kong at
13:4812. 10. Given distance between
13:51the two cities is 2
13:53,572 kilometers and assuming the
13:56plane is moving at constant
13:57speed, calculate said speed. So
14:01here let's highlight the
14:02important things. We have here
14:04some times we have a
14:07distance as stated here and
14:10also constant speed and we
14:12are being asked to calculate
14:13the speed. Perfect. You should
14:16always do this with all
14:17of your questions in physics.
14:18Again, I'm really not joking
14:20unless you're already much further
14:22down the line you're a
14:23vision. You're very confident with
14:24many other questions and you
14:25can just rush through them.
14:27If you don't have the
14:28confidence, do this.
14:30every quantity, every detail, every
14:33assumption in particular, because the
14:35IB will try to trap
14:37you and you need to
14:38be ready to see those
14:39traps. Let's see, it's asking
14:41to calculate speed. Let's recall
14:44the formula for speed. So
14:51distance over time. So looking
14:55at this formula, then we
14:56know that we need two
14:57different variables.
14:58So we need distance and
14:59we need time. We have
15:01our distance. It's right here
15:05And we do have time
15:07we have a starting and
15:08and and time so now
15:10what we need to work
15:11out is a difference in
15:13time between those two moments
15:15so Quite simply here if
15:19we do the difference between
15:2010 hours 10 and 7
15:23Hours 20 then
15:26and we know that that
15:27is for hours 50. However,
15:31we know that we want
15:32a speed, so we want
15:33that answer in meters per
15:36second. We need meters and
15:37we need seconds. Let's start
15:38by converting these. So for
15:40hours 50, let's start by
15:42doing four hours times 60.
15:45So that's for the minutes
15:47that we're going to be
15:48working out. That is 240
15:51minutes, which of course then
15:54we can add
15:54at 240 plus the 50
15:58minutes, that gives us 290
16:00minutes, which we've converted in
16:03seconds by multiplying by 60,
16:07and it gives us 17
16:08,400 seconds. So we have
16:12our seconds now, we need
16:14our meters, we have a
16:15figure in kilometers, we need
16:17to convert that. So 2
16:20,572 times one
16:22on 1000. That gives us
16:25the very big number of
16:282 ,572 ,000 meters. All
16:37right, we have our two
16:39figures here to be clear
16:40this is E. Now that
16:44we have these two, we
16:45just have to grab our
16:47little formula up here and
16:49do our calculation.
16:50Now you make some space
16:52for that. So our speed
16:55is going to be 147
17:01.816 meters per second. If
17:06you have any questions about
17:07this first sample question just
17:09drop a quick message in
17:10the comments. We'll make sure
17:11to answer it. Alright, now
17:13let's see the second sample
17:14question. Ben starts running from
17:17point A at 8 meters
17:18per second.
17:18meters per second. That's quickly
17:20highlight eight meters per second,
17:23from point EME leaves two
17:26seconds later and starts running
17:28perpendicularly to bend at five
17:31meters per second. Ten seconds
17:34after bends are to running,
17:35what is the shortest distance
17:36between the two runners? And
17:38again, we assume constant velocity.
17:40Okay, so this question here
17:43sounds confusing. It's definitely quite
17:46convoluted
17:46then has lots of information
17:48also it's important to highlight
17:52this and correct the mistake.
17:59Anyway, the best way to
18:02approach this question is to
18:03draw a diagram at first.
18:05So we have point A
18:06here and Ben starts running
18:08from point A. So let's
18:11assume Ben starts running in
18:12this direction at a
18:14meters per second. Then two
18:19seconds later, Amy is going
18:21to leave perpendicularly. This is
18:23an important term, it's a
18:24math term, but that is
18:26used very very often in
18:28physics. So, perpendicularly means at
18:3090 degrees. So let's say
18:33that Amy runs in this
18:35direction, we have a 90
18:37degree angle here. Perfect. And
18:40she runs at five meters
18:42per second.
18:42Okay, so we have our
18:45two runners here. We want
18:47the shortest distance between the
18:49two runners after a certain
18:50time. So we know that
18:52they both move in these
18:55two lines and there's 90
18:57degrees between them. So how
18:58do we find a distance,
18:59the shortest distance between two
19:01points, online's like this. It's
19:05a bit of a math
19:06question, but again, physics is
19:07quintessentially math. So you need
19:10to have your math
19:11have knowledge and you're headed
19:12the same time as your
19:13physics knowledge. I know, it's
19:14not easy, but you'll get
19:16better at it, you'll see.
19:19So, how do we calculate
19:20the shortest distance by making
19:22a triangle? Indeed, the shortest
19:26distance between two points like
19:27this is always going to
19:28be a straight line between
19:29the two points. How do
19:30we find that? Well, through
19:32Pythagoras. Indeed, the shortest distance
19:34between two points on lines
19:37like this on perpendicular lines
19:38is always
19:39going to be a straight
19:40line between those points. And
19:42how do we find the
19:44length of that straight line?
19:45Well, as you can see,
19:46this looks a lot like
19:47a right angle triangle. So
19:49we use Pythagoras. Pythagoras, I
19:51remind you, is this. And
19:55therefore, we need a and
19:57b. The length of a,
20:00let's assume a, is how
20:01far Ben ran. So here
20:04is going to be the
20:06distance
20:07That Ben has covered or
20:09the displacement of Ben. Here
20:11it doesn't really matter because
20:13Ben is running in a
20:13straight line. Then for Amy
20:16it's going to be exactly
20:17the same thing. It's going
20:18to be her distance or
20:19her displacement. How do we
20:21find that? Well, let's recall
20:24our speed formula. Or velocity
20:28again. Here it doesn't matter
20:29because we're talking about straight
20:31lines. We remember that this
20:32formula is this
20:35over time. This time we
20:39have speed here 8 meters
20:42per second, 5 meters per
20:43second, and we have time.
20:46So we just need to
20:46do some equation rearranging. So
20:50here I'm going to show
20:51you the shorthand way of
20:52writing the equation, which is
20:55v for velocity equals displacement
20:58over time like this. Most
21:00of the time we're going
21:01to be using velocity in
21:03this place
21:03So that's what I'm going
21:04to use here, but again,
21:06because it's a straight line,
21:08it doesn't really matter. So
21:10using this equation and rearranging,
21:13to solve for displacement, we
21:16have V times T equals
21:18S. Right, well, that's it.
21:20We need to do the
21:21math now. Little warning sign
21:23there. Here, this is an
21:28S for displacement. The reason
21:31why
21:31it's an s is actually
21:32because it comes from the
21:33Latin world for displacement which
21:36I'm not even state here
21:37but all you need to
21:38know is that s is
21:38displacement not time it does
21:40not mean seconds t is
21:42time t is going to
21:43be seconds s is going
21:45to be meters is displacement
21:46very important thing to remember
21:48you can easily get confusing
21:50test and that really will
21:51cost you marks now using
21:53this formula we just have
21:54to find the displacement so
21:56how do we find it
21:57velocity here 8
21:59times 10 because 10 seconds
22:02after Ben started running while
22:03Ben has been running for
22:0410 seconds, which gives us
22:0680 meters. For Amy, there's
22:08a little bit of an
22:09extra step because Amy of
22:11course leaves two seconds later.
22:13That means she has been
22:14running for 10 minus two
22:16seconds. Which of course was
22:20eight, so then we do
22:21eight times five and that
22:23gives us 40 meters. Now
22:25we have our A and
22:27we have our
22:27We're b. We simply use
22:28Pythagoras. I'm going to make
22:30some space for that. Remember
22:32our a equals a, b
22:35equals 40. So, not 40
22:39meters and 80 meters. Units
22:41are important. Within your calculations,
22:43we're getting the units is
22:44not a problem at all.
22:45However, for your final answer,
22:47it's very important. So I
22:48recommend keeping the units throughout
22:51your work. So a squared
22:53plus 40 squared,
22:55So here is our answer
22:5989 .44. Again, we want
23:02three significant figures, so 89
23:05.4. Did you spell it?
23:11Indeed, the units. Do not
23:14forget the units. It's very
23:16important. I just quickly recall
23:17the quantities of motion that
23:18we looked at. There's distance
23:19and displacement both measured in
23:21meters and there's speed and
23:23velocity.
23:23both measured in meters per
23:26second. Okay, so as you
23:29know, when we've already talked
23:30about this, distance in this
23:32placement allow you to calculate
23:35speed and velocity. The only
23:36thing you need apart from
23:38that is of course time.
23:41So let's keep these in
23:43mind. What is graphic motion?
23:45What do you mean by
23:46graphic motion? What we mean
23:48by that is illustrating a
23:50surgeon movement. So
23:51an object moving in a
23:53graphical manner. And there are
23:55two graphs that we're going
23:57to look at. All right,
23:58let's take a look at
23:59a distance time graph. So
24:01a distance time graph is
24:03a graph with distance on
24:04the y -axis and time
24:06on the x -axis. It's
24:08very important that you do
24:09the axis like that. That's
24:10why it's called a distance
24:11time graph or a distance
24:12over time graph. The first
24:14word in the name of
24:15a graph is always going
24:16to be the y -axis
24:17variable at least most of
24:18the time. So what we
24:19are going
24:19To learn today is how
24:22do we build a distance
24:23time graph from a situation?
24:25What does that tell us?
24:26How do we analyze it?
24:27And what exactly does it
24:28represent? That's why I've designed
24:30this little situation here where
24:32Timmy has to go to
24:34school. And for that he
24:35has different sections and his
24:37trip to school he has
24:37three sections. First off he
24:40walks for two minutes and
24:42the distance he covers there
24:43is a hundred meters.
24:47Then he takes a bus
24:50that takes five minutes and
24:54that covers a distance of
24:56400 meters and finally he
24:58walks once again for five
25:00minutes and he covers a
25:01distance of 100 meters. Already
25:02you can see that Timmy
25:04is going much faster in
25:05the first leg of his
25:07trip than when he is
25:08getting close to school. We
25:10can assume that this might
25:11be because he doesn't want
25:12to go to school so
25:13he walks much slower or
25:15maybe he's a
25:16ready to miss the bus
25:17and so he runs for
25:18the first two minutes. Anyway,
25:20that's not very important. But
25:22the important part here is
25:23to understand the situation so
25:25we can graph it. Let's
25:26start by representing this movement
25:28that Timmy has at the
25:30very beginning. So he covers
25:32a hundred meters in two
25:35minutes, which is 120 seconds.
25:37As you can see, the
25:38graph is in seconds and
25:39meters with important with stick
25:41to the units. Always use
25:43SI units in your
25:44Graph, seconds, meters, kilograms, always
25:46use as a SI units.
25:49If you don't know what
25:51SI units are, it's a
25:53very important thing to revise,
25:54I recommend you quickly look
25:55it up because it is
25:56a very simple part of
25:57physics. All right, let's actually
25:59dive into drawing the graph.
26:01As we can see, two
26:03minutes being approximately 120 seconds
26:05means that this leg of
26:07the trip must end around
26:09maybe here.
26:12Alright, well, we can already
26:13draw the first slide of
26:15this graph, then here in
26:16the middle. It goes from
26:18zero, of course, time zero
26:20in distance, zero, it's Timmy's
26:22house. Up to that point.
26:23Now, the next leg lasts
26:26five minutes, which is 300
26:28seconds, and it covers 400
26:31meters. So 400 meters, we
26:33know that added to 100
26:34is 500, so this leg
26:36of the trip must end
26:38around here. And then we
26:39also know
26:40that 5 minutes being 300
26:42seconds means it must and
26:46around here 300 plus 120
26:48seconds from before that gives
26:50us approximately 420 and something
26:53so 420 exact then we
26:55drop point there we go
26:58all right and then all
27:01right well now for the
27:02final leg of the trip
27:03we know that it takes
27:05five minutes so another 300
27:07seconds which
27:08brings us to a grant
27:10total of 720 seconds. So
27:12approximately here. And then another
27:16100 meters, which brings us
27:18to exactly 400 meters. Perfect.
27:23We can draw our last
27:24line of the graph. And
27:27then I'm just going to
27:28make sure we see very
27:29clearly where each leg starts
27:31and finishes. Perfect. All right.
27:32So this is our distance
27:34time graph. Now what
27:36information can we gather here?
27:38Well, I would like to
27:39point out that the equation
27:40of speed or velocity they
27:42are basically identical, so I'm
27:44going to use the same.
27:45Is this one? We have
27:46at the top here, displacement
27:48or distance, and at the
27:49bottom, time. Do you see
27:52it? Do we see speed
27:55somewhere on this graph, or
27:56can we extract it from
27:57this graph? The answer is
27:59yes. It's a gradient. Because
28:02the gradient is always calculated
28:04by rise over run. So
28:06for example, the gradient at
28:08this point is going to
28:09be 200 over, well approximately
28:13250, maybe something like that.
28:15And that is also actually
28:16the gradient of this entire
28:18section because it is a
28:21straight. Then we can also
28:22calculate the gradient here. If
28:23we want to figure out
28:24how fast Timmy was running
28:26to get to the bus
28:26and the gradient here to
28:28calculate how fast Timmy was
28:30walking from the bus stop
28:31to the school.
28:32So this is one of
28:33the most important pieces of
28:35information for a distance time
28:37graph. You must also know
28:38how to build one based
28:39on a situation just like
28:40we did right here. For
28:42a distance time graph that
28:43is mostly everything, you just
28:45need to make sure to
28:46always respect the rules of
28:47making a graph. So always
28:49check the situation beforehand so
28:51you can decide your intervals
28:53here. You can see that
28:54mine were pretty good but
28:56not exactly. For example, the
28:58600 here was unnecessary each
29:00that had been
29:00maybe something like 500 and
29:03also here these two at
29:05the bottom were unnecessary as
29:07the graph did not go
29:08nearly that far. So do
29:10not do that and actually
29:12read the situation, make your
29:14axes, the scale of your
29:16axes in respect to the
29:17situation at hand. All right,
29:19let's move on. All right,
29:20let's take a look at
29:21velocity time graphs now. We're
29:23going to switch it up
29:24a bit and this time
29:25we're going to work from
29:26the graph and deduce the
29:28situation
29:28duration from it. The questions
29:30could ask you either of
29:32those things for either of
29:33the graph types. Alright, so
29:35first off, let's take a
29:37look at this graph and
29:38the different sections it has.
29:40We see that there is
29:42a negative gradient section here.
29:46Here, because it's a velocity
29:47time graph, let's see what
29:49we can deduce from it.
29:51The car here must be
29:53losing velocity because we have
29:55a negative gradient. That
29:56doesn't mean it stopped and
29:58that doesn't mean it's going
30:00backward. This just means that
30:02it is slowing down and
30:04that's the important part. So
30:06the car is still going
30:07in the positive direction because
30:08we have a positive velocity.
30:09It's above the x axis,
30:12but it's slowing down. Then
30:14here it crosses the x
30:18axis. That means the velocity
30:20turns negative. At this point
30:22right here velocity is equal
30:24to zero.
30:24That means a car has
30:26stopped. So for example something
30:29here that we can deduce
30:30is that t equals 20
30:34car stops. So this is
30:38a piece of information we
30:39can deduce. Then the velocity
30:42becomes negative. That means that
30:43the car starts going backwards
30:46after t equals 20. Right
30:49here we see a negative
30:50gradient. Once again, but because
30:52we're below
30:52the x -axis, that means
30:54that the car is actually
30:55speeding up just in the
30:57negative direction. The velocity is
30:59getting more and more negative.
31:01It's magnitude is increasing, but
31:04its direction is negative. Remember
31:07the vectors and scalars a
31:08bit at the beginning of
31:09the lesson? Well, now that
31:10causes a handy. Here, there's
31:12a flat area in the
31:13graph that means constant velocity,
31:15so that means the car
31:18is not changing velocity in
31:19any way. It is maintaining
31:20In this case, negative 3
31:24meters per second velocity. And
31:27then the car starts once
31:29again slowing down. It's still
31:31moving backwards in this region
31:34right here. It's still moving
31:35backwards, but it's slowing down.
31:38We have a positive gradient,
31:39but with a negative value,
31:41which means the magnitude is
31:42decreasing. Then for this bit
31:45here, it is quite normal.
31:47It's increasing means velocity
31:49as increasing the car as
31:50accelerating forwards. Oh, that's a
31:53new word, acceleration. Most of
31:56you should have heard this
31:57before if you've taken physics,
31:58but let's just assume we
32:00need to review it. The
32:01concept of acceleration is the
32:03change in velocity, and that
32:05is very, very important to
32:07keep in mind. The equation
32:08of acceleration, which is not
32:10given in your data booklet,
32:12is the change of velocity
32:14over the change in time.
32:17So acceleration is what we
32:18call the rate of change
32:20of velocity. How much velocity
32:22changes per unit time? So
32:24in the previous distance over
32:25time graph, we saw that
32:27the gradient meant velocity. Well,
32:30similarly here in the velocity
32:31time graph, the gradient means
32:33the acceleration. And you should
32:35be able to understand kind
32:36of why. Because velocity over
32:38time happens to be, well,
32:41exactly the formula for acceleration.
32:43So you can find the
32:44gradient
32:45And then deduce the acceleration
32:47at any point on this
32:50graph. For example, here we
32:52will have a negative acceleration
32:54just like we will here.
32:57Acceleration is also a quantity
32:58that has a direction because
33:00it is based on velocity
33:02that has a direction. All
33:04right. So, acceleration was a
33:06very important part that we
33:08had to quickly look at.
33:09Hopefully you'll understand that again,
33:11as soon as you get
33:12some questions done
33:13It will be much clearer.
33:15Then the second piece of
33:16information that we can actually
33:17extract from this graph is
33:21this placement and this one
33:23is much trickier. So if
33:25you remember earlier and the
33:27lesson we use this formula,
33:28it is simply the velocity
33:30formula rearranged. Here we see
33:32that this placement is actually
33:34the product, so multiplication of
33:36velocity and the time which
33:38happened to actually be here.
33:40We have both values
33:41which means we should be
33:42able to deduce displacement. How
33:44do we do it? Well,
33:47let me answer that question
33:48for you. You find the
33:50area below the graph. Because
33:53how do we find the
33:54area of something, for example,
33:55a square, it's exactly the
33:57same thing on this graph.
33:58You multiply the x -axis
33:59by the y -axis and
34:01then you find the area
34:02below the graph. This is
34:04a concept that is quite
34:05difficult to understand if you
34:07do not have calculus knowledge.
34:09you learn about calculus this
34:11will be a breeze to
34:12understand. For now all you
34:14need to know is that
34:15to find displacement you need
34:17to find the area below
34:20your velocity time graph. So
34:22this area down here for
34:24example is the displacement of
34:27the car between t equals
34:2940 and t equals 80.
34:32Here this is quite a
34:34relatively easy graph to find
34:35the area there between t
34:36equals 40 and t
34:37equals 80, we just have
34:39to find the area of
34:40a triangle. So here we
34:42have 20 at the bottom.
34:45Here on the side we
34:46have 10. So we know
34:48that it's 20 times 10
34:49and because it's a triangle,
34:50we have divided by two,
34:51which actually is really straightforward.
34:54It just gives us actually
34:55my bad. This is not
34:5720. This is 40 and
34:59it's 200. Perfect. So that's
35:00just how you find the
35:01area under the graph and
35:03the display is not poor.
35:04Slightly more complex shapes.
35:05like this right here, you'd
35:07first have to divide the
35:10graph into more easily calculable
35:13areas. For example, here we
35:14have rectangle and then two
35:15triangles, which are much easier
35:17to calculate than this weird
35:20trapezoid type of shape. All
35:22right, that will actually be
35:23it for a velocity time
35:25graph. Now, you might ask
35:27the question, but what if
35:28the graph isn't straight? What
35:29if it's not easy to
35:30calculate? For example, what if
35:32the graph looks like
35:33this. Well, that is actually
35:35a little bit harder to
35:37do and again without calculus
35:38knowledge, it's quite tricky, but
35:40don't worry, I'll explain it.
35:42We'll actually talk about the
35:43slightly curved graphs in the
35:45next section of the class,
35:46but here I can already
35:48show you how to calculate
35:49or more approximate the displacement
35:52in a velocity time graph
35:54that is curved. Here what
35:55you do is you want
35:56to find the area below
35:57the curve. So you divide
35:59the curve
36:01into small rectangles that approximate
36:06the shape of the curve,
36:11etc. etc. etc. etc. etc.
36:18Then you just find the
36:20area of all those rectangles
36:21and you add it together.
36:23And that's how you find
36:25an approximation of the displacement
36:27with a curved graph.
36:29These kinds of questions are
36:31always quite lenient in terms
36:33of the margin of error.
36:34So even if your rectangles
36:36aren't perfect, you should be
36:37getting an answer within the
36:39range of accepted answers if
36:40you do this technique. Again,
36:42I highly recommend you go
36:44practice some questions and if
36:46you still have some doubts,
36:47just drop a comment. Let's
36:48move on to the spontaneous
36:49and average speed. So as
36:51you can see there's a
36:52little example graph here. Most
36:54of the time, you're not
36:55going to have graphs with
36:57straight
36:57lines. That is an ideal
36:59graph. It might happen a
37:00couple times in certain of
37:02your questions, but most of
37:03the time you'll have curved
37:04graphs, just like in real
37:05life. You don't always keep
37:07a constant speed, and that's
37:10the most important thing. Most
37:11of the time, you do
37:12not always go at exactly
37:14the same speed of a
37:15loss. So that's why graphs
37:16distance times graph specifically tend
37:19to look curved. So that's
37:20why there are two terms
37:22that you need to know.
37:23First off, instantaneous speed.
37:25So instantaneous speed just means
37:29speed at a point. Remember
37:34that it's speed at a
37:36given point. So for example,
37:37the instantaneous speed at this
37:40point is going to be
37:42the gradient of the graph
37:43at that point. How do
37:44we find that? We'll find
37:45out in a bit. Average
37:46speed as the name indicates
37:47is the average speed in
37:50a certain interval of time.
37:52So for example, I can
37:53try to calculate
37:54the average speed between t
37:56equals 30 and t equals
37:5940. Now how do we
38:00find those? Well, first off
38:02instantaneous speed is a little
38:04bit tricky because you have
38:05to find the gradient at
38:07that point. How do you
38:09find it? With a tangent
38:11if you have not heard
38:12of those. Those are a
38:17line that exactly just
38:22touches the graph. That line
38:24must pass through that point
38:27and that point only and
38:29it just touches the graph
38:31and goes along. You are
38:32meant to draw these with
38:33a ruler. For example, this
38:34is not a very good
38:35tangent. This is more like
38:37the tangent of maybe this
38:39point. Then once you've drawn
38:40that tangent, you have to
38:42find that gradient, the gradient
38:43of that given tangent. For
38:47example, here we do rise
38:49over run
38:50So the rise here we
38:51can estimate to be approximately
38:5425 and then the run
38:56approximately 18. We find that
38:59green so rise or run
39:01which is approximately 1 .38
39:06under bits. So the instantaneous
39:09speed at that point is
39:12approximately 1 .39 meters per
39:17second. So that's
39:18So speed at that point.
39:20Average speed is quite a
39:21lot simpler. You simply have
39:23to draw a straight line
39:24between the two points, so
39:25the beginning and the end
39:27of your interval, and then
39:29calculate the gradient of that
39:31given line. And there you
39:32get an average speed. So
39:35in this case, we have
39:36very approximately a gradient of
39:384 over 10 approximately. So
39:42that's the average speed, 4
39:44over 10 meters per second.
39:45I hope that
39:46is relatively clear. I know
39:48we're going through this quite
39:48fast, but there is a
39:49lot of content in this
39:50unit and instantaneous average speed
39:53are both concepts that should
39:55be pretty straightforward to understand
39:57once you start doing questions
39:58with them. Let's move on.
40:00Congrats if you've made it
40:01this far in a single
40:02watch. I would expect most
40:04of you to have taken
40:05some breaks in between, but
40:07I promise this is the
40:08last section of this lesson.
40:108 .1 .1 is the
40:12most important section of 8
40:14.1.
40:14point one. The other two
40:16sections that we're going to
40:17be seeing in the next
40:18videos are much, much lighter,
40:20don't worry. So let's take
40:21a look at so that
40:22equation. They are also known
40:24as the kinematic equations. If
40:27you're wondering why they are
40:28called so that well, it's
40:29because those are all the
40:31variables that go into these
40:32equations. Let's take a look
40:34at them. So first we
40:35have s. If you remember
40:37well s is distance or
40:40displacement, but here I'm going
40:42to be talking
40:42about distance. Then u is
40:47initial velocity or speed. v
40:51is final speed or velocity
40:54again. A is acceleration and
41:00finally t is of course
41:02time. All right these are
41:05very important to remember it's
41:06very easy to confuse especially
41:08u and v to remember
41:10these. Now, I need to
41:12state a basic assumption of
41:15servicuations. You can only use
41:17them with constant acceleration. That
41:20means you can only use
41:22it where the speed, time,
41:25graph or velocity, time graph
41:26of the motion you're looking
41:27at is a straight line
41:30with constant gradient, just like
41:31the one here right below
41:33the formula. If there's different
41:35gradients, but they're all straight,
41:37you can always break the
41:37motion down
41:38to different sections like we
41:40did before when we looked
41:41at speed time graphs. Let's
41:43see how we can find
41:45these little variables on our
41:47speed time graph. It's relatively
41:48easy for, for example, initial
41:50and final speed. Initial speed
41:52is of course where the
41:53graph begins right here. Initial
41:56speed camels will be zero.
41:57It can be all the
41:58way at the bottom here.
42:00Then final speed is obviously
42:01where the graph ends. So
42:03we have a u and
42:04then v is going to
42:05be here.
42:06then acceleration if you remember
42:08well is the gradient of
42:10the graph so it's going
42:13to be measured using rise
42:15over run time is of
42:17course just the interval of
42:19your graph so time is
42:21here at the bottom t
42:23and finally distance if you
42:26remember well is the area
42:27under the graph and then
42:30what we need to do
42:31is divide this graph into
42:32a triangle and a rectangle
42:34and find the areas. All
42:36right, let's see how we
42:37do that exactly. So to
42:39find the gradient, we need
42:41to do rise over run.
42:43Here rise is equal to
42:45the minus u. I hope
42:47you see where that comes
42:48from. Then overrun is obviously
42:51t. So v minus u
42:54over t equals acceleration because
42:56it's rise over run. Then
42:59for the area, we divide,
43:01of course, this in a
43:02rectangle and
43:02a triangle. So distance is
43:05equal to the area of
43:07this triangle here which is
43:08one half times the minus
43:11u. Like anyway you're using
43:12the same price, quote unquote,
43:14times t. So that's the
43:16base and the height is
43:17the minus u. And then
43:19plus the rectangle which is
43:20just u times t. Alright.
43:24So that's how we find
43:25all of these variables on
43:27this graph. We have the
43:28gradient which is acceleration. We
43:29have distance, the area on
43:30the
43:30the graph and final and
43:32initial speeds as well as
43:34top. Now we're going to
43:35take a look at how
43:36we derive the kinematic equations.
43:39We can finally look at
43:40them, they're right there in
43:42the middle. Be careful, the
43:44formula booklet actually writes them
43:46in the wrong order. The
43:47fourth one is at the
43:47top and then there's the
43:49first, second, and third. That's
43:50how they're labeled, for example,
43:51in textbooks. So we're going
43:52to look at them in
43:53order, not in formula booklet
43:54order. Without further ado, let's
43:56start with the first equation
43:58of notes.
43:58So the first equation of
44:00motion is just v equals
44:01u plus at and it's
44:03a very, very simple derivation.
44:07As we simply take the
44:09gradient that we got before,
44:11so I will rise over
44:12run and we rearrange this.
44:16That's it. That's the first
44:18equation. The first equation of
44:20motion is the equation that
44:23does not need distance. It
44:25just needs initial and final
44:27velocity, acceleration and time. So
44:29if you have a question
44:30where you're looking for one
44:32of these variables, but you're
44:33lacking distance, then you use
44:36this equation. Perfect. That's it
44:38for the first equation of
44:39motion. The second equation of
44:40motion is the equation for
44:42distance. So here it's quite
44:44obvious what we're going to
44:45do. We're going to look
44:46at the area under the
44:47graph that we had before.
44:51But as you can see,
44:52we have acceleration in this
44:54equation.
44:55So how do we find
44:56that, well, using once again,
44:59our gradient equation here. And
45:03now we can substitute this
45:05back into here. We've derived
45:12the second equation. The first
45:14and second equations are those,
45:16I call the fundamental equations
45:17of motion, because those are
45:18made straight from the information
45:20we get from the graph.
45:21So let's look at the
45:22third equation of motion.
45:23Alright, let's take a look
45:24at this third equation of
45:26motion. This one is the
45:28one that is lacking T,
45:30so it has no time.
45:32And to find that equation,
45:33what we need to do
45:34is use the first and
45:36second that we found just
45:38before. So as we stated
45:44before, this equation doesn't have
45:46time. As both equations have
45:48T, we can rearrange the
45:49first equation so that
45:51it equals t and then
45:54substitute it into the second
45:55equation to get red of
45:57time. So let's begin with
45:58this one and rearranging this
46:02so that it equals t
46:04and then we substitute it
46:06into this formula right here.
46:12And now this is just
46:14pure algebra. Trust me, if
46:17your algebra skills aren't on
46:19point.
46:19It'll be very hard to
46:20get above a 5 in
46:21physics. So work on them,
46:23practice your algebra skills because
46:25they will win you lots
46:27of marks in the exam.
46:29Ideally, you should be doing
46:30this derivation with me or
46:31pause the video, do it
46:32on your own and then
46:33come back for the answers.
46:47Alright, so that is the
46:54derivation. If you have any
46:56questions about the math here,
46:58do drop a comment. I
46:59understand it can be a
47:00little bit complicated. And each
47:01step can demand quite a
47:03bit of algebra. So if
47:04you have any questions, please
47:05don't hesitate to ask. That
47:06is it for derivation of
47:07the third equation of motion,
47:09which as you can see
47:10as a child of the
47:11first two equations. Now for
47:12the fourth equation of motion,
47:14I am going to leave
47:14the task to
47:15you try to derive this
47:17equation. What I can tell
47:18you already is that the
47:20variable it lacks is acceleration.
47:23So you don't need acceleration
47:24or rather, you might have
47:26to get rid of acceleration.
47:28We can however move on
47:29to our final sample question
47:31of this lesson. I know
47:33it's been a marathon. It's
47:34been difficult. Don't worry. We
47:36are there. So this is
47:38a fairly simple question with
47:39super decosions. So a tennis
47:41ball is shot vertically upwards
47:43at
47:43time t0, the ball has
47:46a velocity of 0 at
47:48t equals 5 seconds. Air
47:51resistance is liquid. So here
47:53we need to look at
47:53our variables. We know that
47:56the ball is shot at
47:57t equals 0 and then
47:58at t equals 5 seconds,
48:01the velocity is 0. So
48:04we can say that our
48:06t is equal to 5
48:08and our final velocity is
48:10equal to 0.
48:11So we assume in this
48:13kind of questions that this
48:14is going on on planet
48:15Earth. So we know that
48:17the acceleration is going to
48:19be negative 9 .81 because
48:22the ball is being slowed
48:23down by gravity as it
48:25is shot vertically upwards and
48:26it is the only acceleration
48:28acting on it because air
48:29resistance is negligible. So we're
48:31looking for you, the initial
48:33speed. Let's look at our
48:35equations, which one has all
48:37of these variables, the first
48:38one, first question of inertia.
48:39So the equals u plus
48:42a t, we simply rearranged
48:44the equation to look for
48:45what we want. So the
48:47minus a t equals u,
48:50and then we substitute the
48:52values. Perfect. So again, we
49:01always do answers to three
49:02significant figures. And the proper
49:04way of doing it is
49:06you put your answer here,
49:07with as many digits as
49:08your calculator gives you. And
49:10if it gives you too
49:11many, just add three little
49:12dots like this. And then
49:15you use the approximation here,
49:17equal sign, and you put
49:19your actual answer to three
49:20significant figures. Easy, SUGAT equation.
49:23Lots of them are like
49:24this, though. You might have
49:25to extract more information from
49:26a graph, or maybe do
49:28some extra calculations before you
49:30get to the SUGAT equation.
49:31But most of the questions
49:32will be like this. You
49:33will have certain variables, and
49:34you need to find which
49:35equation actually fits them all
49:37and doesn't need any more
49:39information. Alright, well that will
49:41be it for this lesson.
49:43Finally, we have reached the
49:45end of 1 .1 .1.
49:48You've got all the knowledge
49:49you need, build on this
49:50forward and continue practicing doing
49:52questions. If you have any
49:54additional questions, any doubts, please
49:56drop us a comment and
49:57we'll make sure to answer
49:58and prompt delays. Have a
50:00good rest of your day,
50:01have a good study session
50:03and if by any chance
50:03Thanks for studying for your
50:05exams. Good luck. Hold strong.
50:08You'll get through it.