A scooter starting from rest moves wilth as constant acceleration for a time `/_\t_1`, then with a constant velocity for the next `/_\t_2` and finally with a constant deceleration for the next `/_\t_3` to come to rest. a 500N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter wilthout touching any other part. The force exerted by the seat on the man is

Options

A. 500 N throughout the journey
B. less than 500 N throughout the journey
C. more than 500 N throughtout the journey
D. `gt500 N for time /_\_1 and /_\_3 and 500 N for /_\t_2`.

Answer

To find the force exerted by the seat on the man sitting on the scooter, we need to analyze the three phases of motion of the scooter: acceleration, constant velocity, and deceleration.

### Step-by-Step Solution:

1. **Understanding the Forces Acting on the Man**:
- The man has a weight of 500 N, which acts downwards due to gravity.
- The normal force (N) exerted by the seat acts upwards.

2. **Phase 1: Acceleration (Time \( \Delta t_1 \))**:
- When the scooter accelerates, the man experiences a pseudo force acting in the opposite direction of the acceleration due to the non-inertial frame of reference.
- This pseudo force is equal to \( F_{pseudo} = m \cdot a \), where \( m \) is the mass of the man and \( a \) is the acceleration of the scooter.
- Since the man is at rest with respect to the scooter, the normal force must balance both the weight and the pseudo force:
\[ N = mg + F_{pseudo} \]
- Therefore, the normal force \( N \) is greater than 500 N during this phase.

3. **Phase 2: Constant Velocity (Time \( \Delta t_2 \))**:
- When the scooter moves with constant velocity, there is no acceleration, and thus no pseudo force acting on the man.
- The only force acting on him is his weight, which is balanced by the normal force:
\[ N = mg = 500 \, \text{N} \]
- Therefore, the normal force \( N \) is exactly 500 N during this phase.

4. **Phase 3: Deceleration (Time \( \Delta t_3 \))**:
- Similar to the acceleration phase, when the scooter decelerates, the man again experiences a pseudo force acting in the opposite direction of the deceleration.
- The normal force must again balance both the weight and the pseudo force:
\[ N = mg + F_{pseudo} \]
- Thus, the normal force \( N \) is greater than 500 N during this phase as well.

### Conclusion:
The force exerted by the seat on the man is:
- Greater than 500 N during the acceleration and deceleration phases.
- Equal to 500 N during the constant velocity phase.

Thus, the correct answer is:
**Greater than 500 N for time \( \Delta t_1 \) and \( \Delta t_3 \), and 500 N for \( \Delta t_2 \)**.