Acceleration Examples in Physics

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 m/s10 \text{ m/s} to 30 m/s30 \text{ m/s} in 5 s5 \text{ s}. What is the acceleration?

Answer

a=4 m/s2a = 4 \text{ m/s}^2

First step

1
Use the acceleration formula: a=ΔvΔta = \frac{\Delta v}{\Delta t}.

Full solution

  1. 2
    Substitute the initial and final velocities: a=30−105a = \frac{30 - 10}{5}.
  2. 3
    a=205=4 m/s2a = \frac{20}{5} = 4 \text{ 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 m/s25 \text{ m/s} brakes and comes to rest in 5 s5 \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  m/s20\;\text{m/s} over 40  m40\;\text{m}. (a) Find the acceleration. (b) Find the time it takes.

Example 4

medium
A roller coaster speeds up uniformly from 5  m/s5\;\text{m/s} to 25  m/s25\;\text{m/s} over 40  m40\;\text{m}. Find the acceleration.

Example 5

hard
A car accelerates from rest at a1=3  m/s2a_1=3\;\text{m/s}^2 for 4  s4\;\text{s}, then at a2=2  m/s2a_2=2\;\text{m/s}^2 for 6  s6\;\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  m/s22\;\text{m/s}^2; sprinter B starts 1.5  s1.5\;\text{s} later from rest at 3  m/s23\;\text{m/s}^2. When does B catch A?

Example 7

challenge
A drag racer accelerates uniformly from rest and covers 400  m400\;\text{m} in 8.0  s8.0\;\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 m/s23 \text{ m/s}^2 for 8 s8 \text{ s}. What is the final velocity and distance traveled?

Example 2

medium
A cyclist accelerates uniformly from 4 m/s4 \text{ m/s} to 12 m/s12 \text{ m/s} over 8 seconds8 \text{ seconds}. (a) What is the acceleration? (b) How far does the cyclist travel during this time?

Example 3

easy
A car speeds from 00 to 2020 m/s in 44 s. Find its acceleration.

Example 4

easy
A car slows from 3030 m/s to 1010 m/s in 55 s. Find its acceleration.

Example 5

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

Example 6

easy
A bike accelerates at 22 m/s2^2 from rest. Its velocity after 66 s?

Example 7

easy
Acceleration is −9.8-9.8 m/s2^2 for 22 s on an object initially at 55 m/s up. Find the velocity change.

Example 8

easy
What are the units of acceleration?

Example 9

easy
An object goes from 44 m/s to 44 m/s over 33 s (constant). Acceleration?

Example 10

easy
A car accelerates at 33 m/s2^2. How long to gain 1515 m/s?

Example 11

medium
A car at 88 m/s accelerates at 22 m/s2^2 for 55 s. Find its final velocity.

Example 12

medium
Starting from rest at a=4a=4 m/s2^2, how far does an object travel in 33 s?

Example 13

medium
A car decelerates from 2020 m/s to rest over 5050 m. Find the (constant) acceleration.

Example 14

medium
An object moving at −6-6 m/s has acceleration −2-2 m/s2^2. Is it speeding up or slowing down?

Example 15

medium
A train reaches 4040 m/s from 1010 m/s with acceleration 33 m/s2^2. How long did it take?

Example 16

medium
A car accelerates uniformly from 55 m/s to 2525 m/s in 44 s. Find the distance covered.

Example 17

challenge
A car accelerates from rest at 22 m/s2^2 for 55 s, then holds speed for 55 s. Total distance?

Example 18

challenge
Two cars start together; A accelerates at 22 m/s2^2 from rest, B moves at constant 1010 m/s. When does A catch B?

Example 19

challenge
A ball thrown up at 19.619.6 m/s (g=9.8g=9.8 m/s2^2). Using acceleration reasoning, find the time to reach the highest point.

Example 20

medium
A car accelerates at 2.52.5 m/s2^2 from 1010 m/s. Find its speed after 44 s.

Example 21

medium
An object decelerates uniformly from 2424 m/s to 00 in 66 s. Find the acceleration.

Example 22

medium
From rest at a=6a=6 m/s2^2, find the distance after 22 s.

Example 23

easy
A jogger speeds up from 2  m/s2\;\text{m/s} to 5  m/s5\;\text{m/s} in 6  s6\;\text{s}. Find the acceleration.

Example 24

easy
A skateboarder slows from 8  m/s8\;\text{m/s} to 2  m/s2\;\text{m/s} in 3  s3\;\text{s}. Find the acceleration.

Example 25

easy
A car cruises at a steady 30  m/s30\;\text{m/s} down a straight highway. What is its acceleration?

Example 26

easy
Starting from rest at a=2.5  m/s2a=2.5\;\text{m/s}^2, find the velocity after 4  s4\;\text{s}.

Example 27

easy
An object's acceleration is constant at −3  m/s2-3\;\text{m/s}^2 while moving at +12  m/s+12\;\text{m/s}. Find the velocity 2 s later.

Example 28

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

Example 29

medium
A bike at 10  m/s10\;\text{m/s} accelerates at 1.5  m/s21.5\;\text{m/s}^2 for 6  s6\;\text{s}. Find the distance traveled.

Example 30

medium
A truck decelerates at −1.2  m/s2-1.2\;\text{m/s}^2 from 24  m/s24\;\text{m/s}. How long until it stops, and how far does it travel?

Example 31

medium
An object's velocity changes from −4  m/s-4\;\text{m/s} to +6  m/s+6\;\text{m/s} in 5  s5\;\text{s}. Find its acceleration.

Example 32

medium
A ball is dropped from rest. Using g=9.8  m/s2g=9.8\;\text{m/s}^2, find its speed after 1.5  s1.5\;\text{s}.

Example 33

medium
A car going +8  m/s+8\;\text{m/s} has acceleration −2  m/s2-2\;\text{m/s}^2. After 3  s3\;\text{s} what is its velocity, and is it now moving forward or backward?

Example 34

medium
A car accelerates at 3  m/s23\;\text{m/s}^2 from rest, covers some distance, and reaches 30  m/s30\;\text{m/s}. Find the distance.

Example 35

medium
A toy car accelerates at 0.5  m/s20.5\;\text{m/s}^2 from rest. How long until it has covered 4  m4\;\text{m}?

Example 36

medium
On a velocity-time graph, a straight line rises from 4  m/s4\;\text{m/s} at t=0t=0 to 14  m/s14\;\text{m/s} at t=5  st=5\;\text{s}. Find the acceleration and the distance covered.

Example 37

hard
A car at 20  m/s20\;\text{m/s} brakes with constant deceleration and stops in 50  m50\;\text{m}. Find the deceleration and the stopping time.

Example 38

hard
An elevator accelerates upward at 1.5  m/s21.5\;\text{m/s}^2. A passenger of mass 70  kg70\;\text{kg} stands on a bathroom scale. What reading does the scale show? (Use g=9.8  m/s2g = 9.8\;\text{m/s}^2.)

Example 39

hard
A ball thrown vertically upward leaves the hand at 24  m/s24\;\text{m/s}. Using g=9.8  m/s2g=9.8\;\text{m/s}^2, find the maximum height reached.

Example 40

challenge
An object moves in a circle of radius 2  m2\;\text{m} at a constant speed of 4  m/s4\;\text{m/s}. Find its acceleration.
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Background Knowledge

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

velocity