# Motion

## 05 Average and Instantaneous Acceleration

#### AVERAGE ACCELERATION

• Average acceleration over a period of time is defined as the total change in velocity in the given interval divided by the total time taken for the change.
• For a given interval of time, it is denoted as
$\stackrel{–}{a}$

.

• Mathematically,

Whereandare the instantaneous velocities at timeandandis the average acceleration.

• In the velocity time graph shown above, the slope of the line between any time interval t1 and t2 gives the average value for the rate of change of velocity for the object during the time t1 and t2

#### INSTANTANEOUS ACCELERATION

In a velocity-time curve, the instantaneous acceleration is given by the slope of the tangent on the curve at any instant.

#### POSITIVE, NEGATIVE AND ZERO ACCELERATION

Consider the velocity-time graph shown below:

• Here, between the time intervals of 0 – 2 seconds, the velocity of the particle is increasing with respect to time. In other words, the slope of the v -t curve in this time interval is positive. So it experiences a positive acceleration.
• Between the time intervals of 2 – 3 seconds, the velocity of the object is constant with respect to time. slope of the v -t curve in this time interval is 0. So, the body experiences zero acceleration.
• Consider the time intervals between 3 – 5 seconds. The velocity of the body decreases with respect to time. In other words, the slope of the v -t curve in this time interval is negative. So, the body experiences a negative value of acceleration.