The meaning of acceleration

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.1Sections 2.1

Goal: Say what acceleration is, and recognise speeding up, slowing down and changing direction as acceleration.

01The big picture

An object accelerates whenever its velocity changes. Acceleration is the rate of change of velocity: how much the velocity changes each second.

Velocity is a vector, so acceleration is a vector too. Speeding up, slowing down and changing direction (even at constant speed) are all accelerations. Slowing down is a negative acceleration (a deceleration) when the positive direction is the direction of motion.

Acceleration [paraphrase]: The rate of change of velocity: change in velocity divided by the time taken.
Uniform acceleration [paraphrase]: The velocity changes by the same amount every second.

02Key equations

Acceleration

a = \frac{\Delta v}{\Delta t}

Symbols and units

$a$ acceleration $\mathrm{m\,s^{-2}}$
$\Delta v$ change in velocity $\mathrm{m\,s^{-1}}$
$\Delta t$ time taken $\mathrm{s}$

03Sample problems with solutions

Sample 1 · Speeding up and slowing down
A car speeds up from rest to 24 m s⁻¹ in 8.0 s. Later it slows from 24 m s⁻¹ to 6.0 m s⁻¹ in 3.0 s. Calculate the acceleration in each case.

Speeding up:
$a = \frac{24 - 0}{8.0} = 3.0\ \mathrm{m\,s^{-2}}$
Slowing down: the change in velocity is negative.
$a = \frac{6.0 - 24}{3.0} = -6.0\ \mathrm{m\,s^{-2}}$

Answer: +3.0 m s⁻², then −6.0 m s⁻² (a deceleration of 6.0 m s⁻²)

Unit check:

\frac{\mathrm{m\,s^{-1}}}{\mathrm{s}} = \mathrm{m\,s^{-2}}\ \checkmark

04Practice problems

P1
A sprinter goes from rest to 10 m s⁻¹ in 2.5 s. Calculate the acceleration.
Final answer
4.0 m s⁻²
Answer: 4.0 m s⁻²
P2
A bus slows from 15 m s⁻¹ to 5.0 m s⁻¹ in 4.0 s. Calculate its acceleration.
Final answer
−2.5 m s⁻²
Answer: −2.5 m s⁻²
P3
A train travels at a steady 30 m s⁻¹ in a straight line. What is its acceleration?
Final answer
Zero
Answer: Zero
P4
A car goes round a roundabout at a constant 8.0 m s⁻¹. Is it accelerating? Why?
Final answer
Yes: its direction, so its velocity, changes
Answer: Yes: its direction, so its velocity, changes

05Other useful information

Common mistakes

✗ Wrong: A fast object has a large acceleration.
✓ Right: Acceleration is how quickly the velocity changes, not how big it is.
✗ Wrong: Constant speed means zero acceleration.
✓ Right: Only in a straight line; a change of direction is an acceleration.

Exam tips

Choose a positive direction first; then the sign of $a$ tells you which way it points.

What the syllabus asks

9702 topic 2: define and use acceleration. Coursebook 2.1.

Explore: Practice questions for this lesson