Question

A scooter starting from rest moves at constant acceleration for time $\Delta t_1$, then with a constant velocity for $\Delta t_2$ and finally with a constant deceleration for time $\Delta t_3$ to come to rest. A man of the weight of $200N$ sitting behind the driver manages to be at rest with respect to the scooter without touching any other part of the scooter. The contact force exerted by the seat on the man is

• A. $200N$ throughout the journey.
• B. Less than $200N$ throughout the journey.
• C. More than $200N$ throughout the journey
• D. More than $200N$ for time $\Delta t_1$ and $\Delta t_3$ and $200N$ for $\Delta t_2$

Answer 1

The correct option is D More than $200N$ for time $\Delta t_1$ and $\Delta t_3$ and $200N$ for $\Delta t_2$

As per the question given, the scooter is accelerating and decelerating during the time interval $\Delta t_1$ and $\Delta t_3$ respectively. So, during these times, the scooter and the man has some acceleration and during $\Delta t_2$, the acceleration is zero since velocity is constant.
Now, talking in the frame of scooter, the pseudo force will act on the man during acceleration or deceleration of the scooter. Therefore, to keep the man at rest, seat has to apply the force more than the weight of the man as to counter this pseudo force. For time $\Delta t_2$when scooter is moving with constant velocity, there is no extra force acting on the man. Hence, the seat will exert the equal force as that of man's weight.