Acceleration: Tutorials with Examples

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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 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


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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Updated: 1 January 2013

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