(a)
Given: The mass of the particle is
The position time graph of the particle is shown below:
For
The particle is at rest for
For
The particle has constant position at this time interval. Since the particle does not move, no net force acts on it during this interval.
For
It can be seen in the graph that the position-time graph has constant slope. This means that it has constant velocity. Therefore, the acceleration of the particle is zero and no net force acts on the particle.
(b)
Given: The mass of the particle is
The impulse is given by the change in momentum.
Where,
For
The initial velocity (before point O) is
The final velocity (after point O) is the slope of the line OA.
By substituting the given values in equation (1), we get
Thus, the impulse at
For
The initial velocity (before point A) is the slope of the line OA.
The final velocity (after point A) is
By substituting the given values in equation (1), we get
Thus, the impulse at