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A.1.2—Velocity and acceleration rates

Syllabus
First assessment 2025
Objective
—
Level
HL

Relate Velocity and Acceleration to Rates of Change

Velocity is a rate

Velocity is the rate of change of position:

v⃗=dr⃗dt\vec v=\frac{d\vec r}{dt}

Over a finite interval, average velocity is displacement divided by elapsed time.

Acceleration changes velocity

Acceleration is the rate of change of velocity:

a⃗=dv⃗dt\vec a=\frac{d\vec v}{dt}

A constant acceleration gives equal changes in velocity during equal time intervals.

Read the gradient

On a position–time graph, the gradient represents velocity. On a velocity–time graph, the gradient represents acceleration. The graph’s slope, not its height alone, carries the rate-of-change meaning.

Common trap

Distance divided by time gives average speed, not instantaneous velocity. Likewise, a large velocity does not imply a large acceleration unless the velocity is changing rapidly.

A.1.2 Exam Analysis

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Instantaneous velocity is defined as...

Retrieve the A.1 Kinematics Model

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.