Acceleration

ACCELERATION

Is the rate of change of increase of velocity

OR

Is the change of increase of velocity per unit time

 The SI-unit of acceleration is metre per second square (m/s² or ms^-2)

  

RETARDATION (DECELERATION)

Is the rate of change of decrease of velocity of a body

The deceleration is where the moving body decreases the motion.

NOTE:

The deceleration is negative acceleration

UNIFORM ACCELERATION

Is the constant rate of change of increase of velocity of a body

Example 1

A body accelerates uniformly from a velocity of 30 m/s to 5 m/s in 5 seconds, find acceleration of a body

Solution

Data given

Initial velocity (u) = 30 m/s

Final velocity (v) = 5 m/s

Time (t) = 5 s

Acceleration (a) =?

 

The acceleration of the body = 5 m/s²

  

Example 2

A car brakes and slow down from 20 m/s to 5 m/s in 3 seconds. What is the vehicle acceleration?

Solution

Data given

Initial velocity (u) = 20 m/s

Final velocity (v) = 5 m/s

Time (t) = 3 s

Acceleration (a) =?

 

The acceleration of the vehicle = -5 m/s²

Example 3

An electric train accelerates uniformly from rest to 72 m/s in 6 seconds, calculate the acceleration of the electric train.

Solution

Data given

Initial velocity (u) = 0 m/s

Final velocity (v) =72 m/s

Time (t) = 6 s

Acceleration (a) =?

The acceleration of the body = 12 m/s²

VELOCITY – TIME GRAPH

The velocity – time graph is the line graph of velocity in the vertical axis against time in the horizontal axis.

Hence the slope in the velocity – time graph represent acceleration

NOTE:

The area in the velocity – time graph represented by the total distance travelled.

Example 1

A car accelerates uniformly from rest to 30 m/s in 10 seconds, then maintains the same velocity for 20

seconds and applied brake to a stop in 15 seconds.

a)  Draw a velocity – time graph for the motion of the car.

b)  Determine the acceleration of the car

c)  Calculate the total distance travelled

Solution

a)  

b)  The Acceleration = Slope

 

     The acceleration of the car = 3 m/s²

  

c)  The total distance travelled = Area

 

     The total distance travelled = 975 m

Example 2

A car accelerates from a speed of 40 m/s to a speed of 90 m/s in 15 seconds. It then moves with this speed for 1 minutes and finally decelerates uniformly to a stop after another 20 seconds. Draw the velocity – time graph to represent the motion of the car, then determine;

a)  The maximum speed reached

b)  The acceleration of the car

c)  The deceleration of the car

d)  The total distance travelled by the car

Solution

a)  The maximum speed reached by the car = 90 m/s

b)  The Acceleration = Slope

 

 The acceleration of the car = 2.5 m/s²

c)  The Acceleration = Slope

 

 The deceleration of the car = 2.25 m/s

d)  The total distance travelled = Area A + Area B + Area C

 

The total distance travelled by the car = 8500 m