The velocity (v) – time (t) plot of the motion of a body is shown below :

The acceleration (a) – time (t) graph that best suits this motion is :

Correct Answer:

Step-by-Step Explanation:

Acceleration $a$ is defined as the rate of change of velocity $v$ with respect to time $t$:

$a=\frac{dv}{dt}$

Graphically, the acceleration at any instant is equal to the slope of the velocity-time ($v-t$) curve.

Analyzing the given velocity-time graph segment by segment from left to right:

1. Initial Region (At rest, $v=0$):
The velocity is zero along the time axis, which means slope is zero ($a=0$).

2. First Slanted Line (Increasing Velocity):
The line goes upwards with a constant positive slope.
Since the slope is positive and constant, the acceleration is a constant positive value ($a>0$).

3. Top Horizontal Line (Constant Velocity):
The velocity remains maximum and constant. The slope of a horizontal line is zero.
Therefore, the acceleration during this interval is zero ($a=0$).

4. Second Slanted Line (Decreasing Velocity):
The line goes downwards with a constant negative slope.
Since the slope is negative and constant, the acceleration is a constant negative value ($a<0$).

5. Final Region (At rest, $v=0$):
The velocity returns to zero, giving zero slope ($a=0$).

Putting these parts together, the acceleration-time graph displays a positive rectangular pulse during the acceleration phase and a negative rectangular pulse during the deceleration phase, which corresponds to the graph shown in the correct option.