IB Physics Topic A.1.1 Describing Motion Quantitatively and Qualitatively Revision Notes (SL/HL)

IB Physics Topic A.1.1 Describing Motion Quantitatively and Qualitatively Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

Scalar and Vector Quantities

Scalar: Magnitude Only

Definition

Scalar quantities

Scalar quantities have only magnitude and no direction.

It tells you how much of something there is, but not where or in which direction.

Common examples include:

Distance: The total length of the path traveled, regardless of direction.
Speed: How fast an object is moving, without considering its direction.
Time: A measure of duration.

Example

For instance, if you walk a total of 5 km along a circular path and return to your starting point, your total distance is 5 km, even though you haven’t changed your position.

Vectors: Magnitude and Direction

Definition

Vector quantities

Vector quantities have both magnitude and direction.

This makes it more descriptive than a scalar. Examples include:

Displacement: The straight-line distance between an object’s starting and ending points, along with the direction.
Velocity: The rate of change of displacement, including direction.
Acceleration: The rate of change of velocity, including direction.

Example

Returning to the road trip example, if you drive 100 km north and then 100 km east, your displacement is the straight-line distance from your starting point to your final position, along with the direction (northeast).

The Role of Projections

While vector quantities contain both magnitude and direction, many physical analyses require expressing how much of a vector acts along a specific axis, such as the x-axis or y-axis.
This is done through a process called projection, which transforms a vector into a scalar component aligned with a chosen direction.

Calculating and Using Scalar Projections

To determine the scalar projection of a vector onto a chosen axis, one must identify the angle between the vector and the axis and apply the cosine or sine function.

In Cartesian coordinates, if the axis of interest aligns with, for example, the $x$-axis, then the scalar projection corresponds simply to the $x$-component of the vector.
1. This is typically expressed as $A_x = |\vec{A}|\cos\theta$, where $\theta$ is the angle between $\vec{A}$ and the positive $x$-direction.
If the axis of interest is the $y$-axis, then the scalar projection corresponds to the $y$-component of the vector.
1. Correspondingly, this is typically expressed as $A_y = |\vec{A}|\sin\theta$, where $\theta$ is the angle between $\vec{A}$ and the positive $x$-axis.

A scalar projection represents the magnitude of the vector's influence along an axis and carries a sign that indicates direction.

A positive projection means the vector points in the same direction as the defined positive axis.
A negative projection indicates that it points in the opposite direction.

Example

This sign is physically meaningful.
For instance, a negative projection of acceleration along an axis implies that the acceleration is directed against the chosen positive direction.
It is an important consideration when analyzing situations such as deceleration or motion reversal.

Note

Understanding projections is essential for correctly applying kinematic and dynamic equations, as it allows us to bridge the directional nature of vectors with the scalar quantities used in one-dimensional calculations.
You apply this resolution into components directly in A.1.3 (projectile motion); vectors are also treated as a core skill in the dedicated vectors article.

Comparing Scalars and Vectors

Quantity	Scalar	Vector
Distance vs. Displacement	Total path length	Straight-line change in position
Speed vs. Velocity	Magnitude of velocity	Speed with direction
Energy	Always scalar	N/A

Speed and Velocity: Comparing Two Measures of Motion

Average Speed and Average Velocity

Both speed and velocity describe how fast something is moving, but they differ in their treatment of direction.

Definition

Average speed

Average speed is the total distance traveled divided by the total time taken. It’s a scalar quantity.

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Note

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Lorem ipsum dolor sit amet, consectetur adipiscing elit.
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Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

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Scalar and Vector Quantities

Scalar: Magnitude Only

Definition

Scalar quantities

Scalar quantities have only magnitude and no direction.

It tells you how much of something there is, but not where or in which direction.

Common examples include:

Distance: The total length of the path traveled, regardless of direction.
Speed: How fast an object is moving, without considering its direction.
Time: A measure of duration.

Example

For instance, if you walk a total of 5 km along a circular path and return to your starting point, your total distance is 5 km, even though you haven’t changed your position.

Vectors: Magnitude and Direction

Definition

Vector quantities

Vector quantities have both magnitude and direction.

This makes it more descriptive than a scalar. Examples include:

Displacement: The straight-line distance between an object’s starting and ending points, along with the direction.
Velocity: The rate of change of displacement, including direction.
Acceleration: The rate of change of velocity, including direction.

Example

The Role of Projections

While vector quantities contain both magnitude and direction, many physical analyses require expressing how much of a vector acts along a specific axis, such as the x-axis or y-axis.
This is done through a process called projection, which transforms a vector into a scalar component aligned with a chosen direction.

Calculating and Using Scalar Projections

To determine the scalar projection of a vector onto a chosen axis, one must identify the angle between the vector and the axis and apply the cosine or sine function.

In Cartesian coordinates, if the axis of interest aligns with, for example, the $x$-axis, then the scalar projection corresponds simply to the $x$-component of the vector.
1. This is typically expressed as $A_x = |\vec{A}|\cos\theta$, where $\theta$ is the angle between $\vec{A}$ and the positive $x$-direction.
If the axis of interest is the $y$-axis, then the scalar projection corresponds to the $y$-component of the vector.
1. Correspondingly, this is typically expressed as $A_y = |\vec{A}|\sin\theta$, where $\theta$ is the angle between $\vec{A}$ and the positive $x$-axis.

A scalar projection represents the magnitude of the vector's influence along an axis and carries a sign that indicates direction.

A positive projection means the vector points in the same direction as the defined positive axis.
A negative projection indicates that it points in the opposite direction.

Example

This sign is physically meaningful.
For instance, a negative projection of acceleration along an axis implies that the acceleration is directed against the chosen positive direction.
It is an important consideration when analyzing situations such as deceleration or motion reversal.

Note

Understanding projections is essential for correctly applying kinematic and dynamic equations, as it allows us to bridge the directional nature of vectors with the scalar quantities used in one-dimensional calculations.
You apply this resolution into components directly in A.1.3 (projectile motion); vectors are also treated as a core skill in the dedicated vectors article.

Comparing Scalars and Vectors

Quantity	Scalar	Vector
Distance vs. Displacement	Total path length	Straight-line change in position
Speed vs. Velocity	Magnitude of velocity	Speed with direction
Energy	Always scalar	N/A

Speed and Velocity: Comparing Two Measures of Motion

Average Speed and Average Velocity

Both speed and velocity describe how fast something is moving, but they differ in their treatment of direction.

Definition

Average speed

Average speed is the total distance traveled divided by the total time taken. It’s a scalar quantity.

Definition

Paywall

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Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics A.1.1 Describing Motion Quantitatively and Qualitatively Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Scalar and Vector Quantities

Scalar: Magnitude Only

Vectors: Magnitude and Direction

The Role of Projections

Calculating and Using Scalar Projections

Comparing Scalars and Vectors

Speed and Velocity: Comparing Two Measures of Motion

Average Speed and Average Velocity

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Scalar and Vector Quantities

Scalar: Magnitude Only

Vectors: Magnitude and Direction

The Role of Projections

Calculating and Using Scalar Projections

Comparing Scalars and Vectors

Speed and Velocity: Comparing Two Measures of Motion

Average Speed and Average Velocity

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account