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.
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 v_{0} at time t_{0} and final velocity v at time t has an average acceleration between t_{0} and t given by
or
average acceleration = 
change in velocity
change in time

= 

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 = 

= 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/s^{2}?
Solution:
The initial velocity is 0 (from rest) and the final velocity is 36 km/h. Hence
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 = 

= 0.5 m/s^{2}

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/s^{2}?
Solution:
The initial velocity is 72 km/h and the final velocity is 0 (rest). Hence
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 = 

= 0.8 m/s^{2}

Example 4: A plane has a take off speed of 300 km/h. What is the acceleration in m/s^{2} 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
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 = 

= 1.85 m/s^{2}

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 = 36 * 1000 m / 3600 s = 10 m/s
average acceleration = 

= 0.4 m/s^{2}

Example 6:Starting with a constant velocity of 50 km/h, a car accelerates for 32 seconds at an acceleration of 0.5 m/s^{2} . 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/s^{2} =


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/s^{2}?
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/s^{2} =


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
