IB Physics kinematics explains how objects move using position, displacement, velocity and acceleration. For exams, the topic centres on a small set of highly testable skills: interpreting motion graphs, choosing and applying constant-acceleration equations, resolving projectile motion into components, and reasoning about fluid resistance.
Kinematics is A.1 within the current IB Physics theme Space, time and motion. The core A.1 content applies to both SL and HL, so the fundamental expectations are the same. The challenge is rarely recalling an equation alone. It is translating the wording, graph or physical situation into a correct model and then presenting enough working to earn every available mark.
The quantities you must distinguish
Many kinematics errors begin before any calculation. Examiners expect you to distinguish scalar quantities, which have magnitude only, from vector quantities, which have magnitude and direction.
| Quantity | Scalar or vector? | Meaning | SI unit |
|---|---|---|---|
| Distance | Scalar | Total path length travelled | m |
| Displacement | Vector | Change in position from start to finish | m |
| Speed | Scalar | Rate of change of distance | m s^-1 |
| Velocity | Vector | Rate of change of position | m s^-1 |
| Acceleration | Vector | Rate of change of velocity | m s^-2 |
A runner completing one full 400 m lap travels a distance of 400 m but has zero displacement because the final position is the initial position. Consequently, the average speed is not zero, while the average velocity is zero.
Average and instantaneous values
Average velocity is total displacement divided by elapsed time:
average velocity = displacement / time
Instantaneous velocity is the velocity at one particular moment. On a position-time graph, it is found from the gradient of the tangent at that moment. Similar distinctions apply to speed and acceleration, so read carefully when a question asks for an average rather than an instantaneous value.
A negative velocity does not mean that an object is slowing down. It means the object is moving in the direction defined as negative. An object with negative velocity and negative acceleration is increasing its speed because both vectors point in the same direction.
How to read kinematics graphs
Graphs test whether you understand the physical meaning behind the mathematics. Before calculating anything, read the axis labels and units.
| Graph | Gradient represents | Area represents |
|---|---|---|
| Position against time | Velocity | No standard kinematics quantity |
| Velocity against time | Acceleration | Displacement |
| Acceleration against time | Rate of change of acceleration | Change in velocity |
On a position-time graph, a horizontal line indicates that position is constant, so the object is stationary. A straight sloping line represents constant velocity, while a changing gradient represents acceleration.
On a velocity-time graph, a horizontal line represents constant velocity and zero acceleration. A straight non-horizontal line represents constant acceleration. The signed area between the graph and the time axis gives displacement, so an area below the axis contributes a negative displacement.
Exam method for graph questions
When asked to determine acceleration from a velocity-time graph:
- Select two well-separated points on the line or tangent.
- Calculate change in velocity divided by change in time.
- Include the sign and unit m s^-2.
- Avoid using coordinates read from a thick or curved part of the graph unless you have drawn a tangent.
When asked to determine displacement, divide the area into rectangles, triangles or trapezia. If the graph is curved, the question may require an estimate by counting squares or approximating the area geometrically.
The constant-acceleration equations
The current IB Physics data booklet provides four equations for uniformly accelerated motion:
- s = ((u + v) / 2)t
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as
Here, s is displacement, u is initial velocity, v is final velocity, a is constant acceleration and t is elapsed time. These equations apply only when acceleration is uniform over the interval being considered.
The data booklet presents equations without vector notation, so you must supply direction through signs. Choose a positive direction, state it when the situation is not obvious, and assign every vector quantity a consistent sign.
A reliable equation-selection method
Write down the five variables s, u, v, a, t. Insert the known values with signs, identify the required variable, and select the equation that excludes the remaining unknown.
For example, a ball is thrown vertically upward at 18 m s^-1. Ignoring air resistance, find its maximum height above the release point using g = 9.81 m s^-2.
Take upward as positive:
- u = +18 m s^-1
- v = 0 at maximum height
- a = -9.81 m s^-2
- s = unknown
Using v^2 = u^2 + 2as:
0 = 18^2 + 2(-9.81)s
s = 16.5 m to three significant figures.
The final velocity is zero only at that instant. The acceleration remains -9.81 m s^-2 because gravity still acts at the highest point.
Projectile motion
For a projectile moving without fluid resistance, horizontal and vertical motion can be analysed independently. They share the same time but have different velocities and accelerations.
| Component | Horizontal | Vertical |
|---|---|---|
| Acceleration | 0 | -g if upward is positive |
| Velocity | Constant | Changes uniformly |
| Useful model | x = u_x t | Constant-acceleration equations |
For a launch speed u at angle θ above the horizontal:
- u_x = u cos θ
- u_y = u sin θ
Calculate the time using the vertical motion, then use that same time in the horizontal calculation. Do not insert the total launch speed into both directions.
For a projectile returning to its original height without air resistance, the vertical component of its final velocity has the same magnitude as its initial vertical component but the opposite direction. This symmetry does not apply when the landing height differs from the launch height or when fluid resistance is significant.
At the highest point, vertical velocity is zero, but horizontal velocity is not. The projectile therefore still has a non-zero total velocity unless it was launched vertically. Its acceleration is still vertically downward with magnitude g.
Fluid resistance and terminal speed
IB questions also test the qualitative effect of fluid resistance. Drag acts opposite to the direction of motion and normally increases as speed increases.
For a falling object released from rest, drag is initially zero or negligible because the speed is zero. The weight produces a downward resultant force, so the object accelerates. As speed increases, upward drag increases, reducing the resultant force and acceleration.
At terminal speed, drag balances weight. The resultant force and acceleration are zero, but velocity is not zero. The object continues downward at constant speed.
Air resistance also destroys the simple symmetry of ideal projectile motion. It generally reduces maximum height, range and speed compared with the no-drag model. A qualitative trajectory should usually be drawn lower and with a steeper descending section than the ideal parabola.
How IB exam questions phrase kinematics tasks
Command terms indicate the type and depth of response required. Treat them as instructions rather than interchangeable verbs.
| Command term | What your answer should contain |
|---|---|
| State | A brief value, fact or conclusion without explanation |
| Calculate | Relevant numerical working and a final answer with units |
| Determine | A result reached using the supplied information, often including graph work |
| Describe | A detailed account of what happens or what a graph shows |
| Explain | Causes, mechanisms or physical reasoning connecting evidence to a conclusion |
| Draw | An accurate, labelled graph or diagram, normally using a ruler where appropriate |
| Estimate | A reasonable approximate result with visible assumptions or graphical method |
A question saying “calculate the acceleration” requires substitution and working. A question saying “explain why the acceleration decreases” requires a force-based argument, such as increasing drag reducing the resultant force. Giving only a numerical pattern for an explanation question may not address the command term.
A mark-focused method for calculations
Use the following sequence under exam conditions:
- Define the direction. Write “upward positive” or mark the chosen direction on a sketch.
- List known quantities. Include signs and convert units before substitution.
- Check the model. Decide whether acceleration is constant and whether resistance is neglected.
- Choose the equation. Select it from the variables rather than from memory alone.
- Show substitution. Method marks may remain available even if arithmetic later goes wrong.
- Give units and sensible precision. Avoid excessive calculator digits.
- Check the physics. Ask whether the sign, magnitude and direction are reasonable.
The most valuable next step is seeing this method used on complete questions. RevisionDojo’s A.1 Kinematics worked videos show how individual exam-style problems are translated into equations, diagrams and mark-earning working. Pair these with the kinematics Questionbank so that watching a solution is followed immediately by solving a similar problem independently.
Common mistakes that cost marks
- Treating distance and displacement as interchangeable.
- Assuming negative acceleration always means slowing down.
- Using a constant-acceleration equation when acceleration varies.
- Forgetting that area under a velocity-time graph is signed.
- Setting acceleration to zero at the top of a projectile’s path.
- Mixing horizontal and vertical projectile components.
- Using g as positive while also taking upward as positive.
- Confusing terminal speed with zero velocity.
- Reporting a number without units or visible working.
- Describing what happens when the command term requires an explanation of why.
One efficient correction routine is to classify each error as conceptual, setup, algebra, graph interpretation or communication. Use the IB Physics topic hub to review the relevant idea, then retest it through the broader IB Physics Questionbank. Timed Physics predicted papers can then test whether the method remains reliable when kinematics is mixed with forces, momentum and energy.
Conclusion
IB Physics kinematics is built around a manageable set of ideas, but exam success depends on applying them precisely. Distinguish vectors from scalars, interpret gradients and areas correctly, use constant-acceleration equations only under valid conditions, separate projectile components, and explain drag through resultant force.
Revision should move from understanding to worked examples and then independent timed practice. RevisionDojo’s kinematics notes, Questionbank, Jojo AI feedback and per-question worked videos can support that sequence, with mock or predicted papers used once the individual skills are secure.
