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/s2 * 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/s2 * 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/s2) = 13.8 seconds

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