# Acceleration: Tutorials with Examples

Examples with explanations on the concepts of acceleration of moving object are presented. More problems and their solutions can also be found in this website.

## Average Acceleration

The average acceleration is a vector quantity (magnitude and direction) that describes the rate of change (with the time) of the velocity of a moving object.

An object with initial velocity v0 at time t0 and final velocity v at time t has an average acceleration between t0 and t given by

 average acceleration = v - v0 t - t0
or
 average acceleration = change in velocity change in time = Δv Δt

## Examples with soltutions

### Example 1

What is the acceleration of an object that moves with uniform velocity?
Solution:
If the velocity is uniform, let us say V, then the initial and final velocities are both equal to V and the definition of the acceleration gives
 average acceleration = V - V t - t0 = 0

The acceleration of an object moving at a constant velocity is equal to 0.

### Example 2

A car accelerates from rest to a speed of 36 km/h in 20 seconds. What is the acceleration of the car in m/s2?
Solution:
The initial velocity is 0 (from rest) and the final velocity is 36 km/h. Hence
 average acceleration = 36 km/h - 0 20 seconds = 36 km/h 20 seconds

We now convert 36 km/h into m/s as follows

36 km/h = 36 * 1000 m / 3600 s = 10 m/s

Hence
 average acceleration = 10 m/s 20 seconds = 0.5 m/s2

### Example 3

A car slows down from a speed of 72 km/h to rest in 25 seconds. What is the acceleration of the car in m/s2?
Solution:
The initial velocity is 72 km/h and the final velocity is 0 (rest). Hence
 average acceleration = 0-72 km/h 25 seconds = -72 km/h 25 seconds

We now convert 72 km/h into m/s as follows

36 km/h = 72 * 1000 m / 3600 s = 20 m/s

Hence
 average acceleration = - 20 m/s 25 seconds = -0.8 m/s2

### Example 4

A plane has a take off speed of 300 km/h. What is the acceleration in m/s2 of the plane if the plane started from rest and took 45 seconds to take off?
Solution:
The initial velocity is 0 (from rest) and the final velocity is 300 km/h (take off). Hence
 average acceleration = 300 km/h - 0 45 seconds = 300 km/h 45 seconds

We now convert 300 km/h into m/s as follows

300 km/h = 300 * 1000 m / 3600 s = 83.3 m/s

Hence
 average acceleration = 83.3 m/s 45 seconds = 1.85 m/s2

### Example 5

What acceleration is needed to accelerate a car from 36 km/h to 72 km/h in 25 seconds?
Solution:
The initial velocity is 36 km/h and the final velocity is 72 km/h, hence
 average acceleration = 72 km/h - 36 km/h 25 seconds = 36 km/h 25 seconds

36 km/h = 36 * 1000 m / 3600 s = 10 m/s
 average acceleration = 10 m/s 25 seconds = 0.4 m/s2

### Example 6

Starting with a constant velocity of 50 km/h, a car accelerates for 32 seconds at an acceleration of 0.5 m/s2 . What is the velocity of the car at the end of the period of 32 seconds of acceleration?
Solution:
50 km/h is the initial velocity; we are given the acceleration and we asked to find the final velocity.
 average acceleration = 0.5 m/s2 = V - 50 km/h 32 second

The above equation can be written as
V - 50 km/h = 0.5 m/s
2 * 32 s = 16 m/s
convert 16 m/s into km/h
16 m/s = 16 m * (1km/1000m) / (1s * 1h/3600 s) = 16 * 3600 / 1000 km/h = 57.6 km/h
V = 57.6 km/h + 50 km/h = 107.6 km/h

### Example 7

How long does it take to accelerate a car from a speed of 50 km/h to a speed of 100 km/h at an acceleration of 1 m/s2?
Solution:
The initial velocity is 50 km/h and the final velocity is 100 km/h and we are given the acceleration
 average acceleration = 1 m/s2 = 100 km/h - 50 km/h t

The above equation gives the equation
1 m/s
2 * t = 50 km/h
50 km/h = 50 km (1000 m / 1 km) / (1h * (3600 s / 1 h)) = 13.8 m/s
t = (13.8 m/s) / (1 m/s
2) = 13.8 seconds