Acceleration Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Acceleration.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The rate at which an object's velocity changes over time, measured in metres per second squared (m/s²).

How quickly your speed (or direction) is changing. The 'push back' you feel when a car speeds up.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Acceleration starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to acceleration but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy

A car accelerates from

10 \text{ m/s}

30 \text{ m/s}

5 \text{ s}

. What is the acceleration?

Answer

a = 4 {m/s}^{2}

First step

Use the acceleration formula:

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

Full solution

2
Substitute the initial and final velocities: $a = \frac{30 - 10}{5}$ .
3
$a = \frac{20}{5} = 4 {m/s}^{2}$

Acceleration is the rate of change of velocity. A positive acceleration means the object is speeding up in the positive direction.

Example 2

medium

A car traveling at

25 \text{ m/s}

brakes and comes to rest in

5 \text{ s}

. What is the deceleration, and how far does it travel while braking?

Example 3

medium

A car accelerates uniformly from rest to

20\;\text{m/s}

over

40\;\text{m}

. (a) Find the acceleration. (b) Find the time it takes.

Example 4

medium

A roller coaster speeds up uniformly from

5\;\text{m/s}

25\;\text{m/s}

over

40\;\text{m}

. Find the acceleration.

Example 5

hard

A car accelerates from rest at

a_1=3\;\text{m/s}^2

for

4\;\text{s}

, then at

a_2=2\;\text{m/s}^2

for

6\;\text{s}

. Find its final velocity and total distance traveled.

Example 6

hard

Two sprinters start side-by-side. Sprinter A accelerates from rest at

2\;\text{m/s}^2

; sprinter B starts

1.5\;\text{s}

later from rest at

3\;\text{m/s}^2

. When does B catch A?

Example 7

challenge

A drag racer accelerates uniformly from rest and covers

400\;\text{m}

8.0\;\text{s}

. Find (a) the acceleration and (b) the top speed.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

An object starts from rest and accelerates at

3 \text{ m/s}^2

for

8 \text{ s}

. What is the final velocity and distance traveled?

Example 2

medium

A cyclist accelerates uniformly from

4 \text{ m/s}

12 \text{ m/s}

over

8 \text{ seconds}

. (a) What is the acceleration? (b) How far does the cyclist travel during this time?

Example 3

easy

A car speeds from

0

20

m/s in

4

s. Find its acceleration.

Example 4

easy

A car slows from

30

m/s to

10

m/s in

5

s. Find its acceleration.

Example 5

easy

An object's velocity is constant. What is its acceleration?

Example 6

easy

A bike accelerates at

2

m/s

^2

from rest. Its velocity after

6

Example 7

easy

Acceleration is

-9.8

m/s

^2

for

2

s on an object initially at

5

m/s up. Find the velocity change.

Example 8

easy

What are the units of acceleration?

Example 9

easy

An object goes from

4

m/s to

4

m/s over

3

s (constant). Acceleration?

Example 10

easy

A car accelerates at

3

m/s

^2

. How long to gain

15

m/s?

Example 11

medium

A car at

8

m/s accelerates at

2

m/s

^2

for

5

s. Find its final velocity.

Velocity addition: 8 m/s + 10 m/s gained over 5 s = final velocity

Example 12

medium

Starting from rest at

a=4

m/s

^2

, how far does an object travel in

3

Example 13

medium

A car decelerates from

20

m/s to rest over

50

m. Find the (constant) acceleration.

Example 14

medium

An object moving at

-6

m/s has acceleration

-2

m/s

^2

. Is it speeding up or slowing down?

Example 15

medium

A train reaches

40

m/s from

10

m/s with acceleration

3

m/s

^2

. How long did it take?

Example 16

medium

A car accelerates uniformly from

5

m/s to

25

m/s in

4

s. Find the distance covered.

Example 17

challenge

A car accelerates from rest at

2

m/s

^2

for

5

s, then holds speed for

5

s. Total distance?

Example 18

challenge

Two cars start together; A accelerates at

2

m/s

^2

from rest, B moves at constant

10

m/s. When does A catch B?

Example 19

challenge

A ball thrown up at

19.6

m/s (

g=9.8

m/s

^2

). Using acceleration reasoning, find the time to reach the highest point.

Example 20

medium

A car accelerates at

2.5

m/s

^2

from

10

m/s. Find its speed after

4

Example 21

medium

An object decelerates uniformly from

24

m/s to

0

6

s. Find the acceleration.

Example 22

medium

From rest at

a=6

m/s

^2

, find the distance after

2

Example 23

easy

A jogger speeds up from

2\;\text{m/s}

5\;\text{m/s}

6\;\text{s}

. Find the acceleration.

Example 24

easy

A skateboarder slows from

8\;\text{m/s}

2\;\text{m/s}

3\;\text{s}

. Find the acceleration.

Example 25

easy

A car cruises at a steady

30\;\text{m/s}

down a straight highway. What is its acceleration?

Example 26

easy

Starting from rest at

a=2.5\;\text{m/s}^2

, find the velocity after

4\;\text{s}

Example 27

easy

An object's acceleration is constant at

-3\;\text{m/s}^2

while moving at

+12\;\text{m/s}

. Find the velocity 2 s later.

Opposing acceleration reduces velocity from 12 m/s to 6 m/s after 2 s

Example 28

easy

An object near Earth's surface is in free fall. What is its acceleration?

Example 29

medium

A bike at

10\;\text{m/s}

accelerates at

1.5\;\text{m/s}^2

for

6\;\text{s}

. Find the distance traveled.

Example 30

medium

A truck decelerates at

-1.2\;\text{m/s}^2

from

24\;\text{m/s}

. How long until it stops, and how far does it travel?

Example 31

medium

An object's velocity changes from

-4\;\text{m/s}

+6\;\text{m/s}

5\;\text{s}

. Find its acceleration.

Example 32

medium

A ball is dropped from rest. Using

g=9.8\;\text{m/s}^2

, find its speed after

1.5\;\text{s}

Example 33

medium

A car going

+8\;\text{m/s}

has acceleration

-2\;\text{m/s}^2

. After

3\;\text{s}

what is its velocity, and is it now moving forward or backward?

Example 34

medium

A car accelerates at

3\;\text{m/s}^2

from rest, covers some distance, and reaches

30\;\text{m/s}

. Find the distance.

Example 35

medium

A toy car accelerates at

0.5\;\text{m/s}^2

from rest. How long until it has covered

4\;\text{m}

Example 36

medium

On a velocity-time graph, a straight line rises from

4\;\text{m/s}

t=0

14\;\text{m/s}

t=5\;\text{s}

. Find the acceleration and the distance covered.

Example 37

hard

A car at

20\;\text{m/s}

brakes with constant deceleration and stops in

50\;\text{m}

. Find the deceleration and the stopping time.

Example 38

hard

An elevator accelerates upward at

1.5\;\text{m/s}^2

. A passenger of mass

70\;\text{kg}

stands on a bathroom scale. What reading does the scale show? (Use

g = 9.8\;\text{m/s}^2

Example 39

hard

A ball thrown vertically upward leaves the hand at

24\;\text{m/s}

. Using

g=9.8\;\text{m/s}^2

, find the maximum height reached.

Example 40

challenge

An object moves in a circle of radius

2\;\text{m}

at a constant speed of

4\;\text{m/s}

. Find its acceleration.

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Related Concepts

Velocity Force Newton's Second Law

Background Knowledge

These ideas may be useful before you work through the harder examples.

velocity