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, including changes in speed or direction.

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 is the derivative of velocity, the second derivative of position.

Common stuck point: Negative acceleration can mean slowing down OR speeding up backward.

Worked Examples

Example 1

easy
A car accelerates from 10 \text{ m/s} to 30 \text{ m/s} in 5 \text{ s}. What is the acceleration?

Solution

  1. 1
    Use the acceleration formula: a = \frac{\Delta v}{\Delta t}.
  2. 2
    Substitute the initial and final velocities: a = \frac{30 - 10}{5}.
  3. 3
    a = \frac{20}{5} = 4 \text{ m/s}^2

Answer

a = 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 \text{ m/s} brakes and comes to rest in 5 \text{ s}. What is the deceleration, and how far does it travel while braking?

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} to 12 \text{ m/s} over 8 \text{ seconds}. (a) What is the acceleration? (b) How far does the cyclist travel during this time?
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Background Knowledge

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

velocity