Question: 36. The velocity (v) – time (t) plot of the motion of a body is shown below :
Answer: Option (3)
Explanation:
The acceleration of a body is given by the slope of the velocity–time graph,
that is a = \frac{dv}{dt}.
In the given velocity–time graph, the velocity first increases linearly with time,
so the slope of the graph is positive and constant.
Hence, the acceleration is constant and positive during this interval.
After this, the velocity becomes constant with time,
which means the slope of the velocity–time graph is zero.
Therefore, the acceleration during this interval is zero.
Finally, the velocity decreases linearly with time,
so the slope of the velocity–time graph is negative and constant.
Hence, the acceleration is constant and negative during this interval.
Thus, the acceleration–time graph must show a positive constant acceleration for some time,
followed by zero acceleration, and then a constant negative acceleration.
This corresponds to option (3).