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 with resect 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 solve the problem, we need to analyze the motion of the scooter and the forces acting on the man sitting on it throughout the different phases of motion: acceleration, constant velocity, and deceleration.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Man:**
- The man sitting on the scooter experiences two main forces:
- The gravitational force acting downwards (weight), \( F_g = mg \).
- The normal force exerted by the seat on the man, \( N \), acting upwards.

2. **Calculate the Weight of the Man:**
- Given the mass of the man is \( m = 50 \, \text{kg} \).
- The weight \( F_g \) is calculated as:
\[ F_g = mg = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N} \]

3. **Analyze the Motion Phases:**
- **Phase 1: Constant Acceleration (time \( t_1 \))**
- During this phase, the man experiences an upward normal force and a downward gravitational force. However, since the scooter is accelerating, the man will feel a pseudo-force acting in the opposite direction of the acceleration.
- The net force in the vertical direction is still balanced, so:
\[ N - mg = 0 \implies N = mg \]

- **Phase 2: Constant Velocity (time \( t_2 \))**
- When the scooter moves with constant velocity, there is no acceleration. The forces acting on the man are again balanced:
\[ N - mg = 0 \implies N = mg \]

- **Phase 3: Constant Deceleration (time \( t_3 \))**
- Similar to the acceleration phase, during deceleration, the man will again feel a pseudo-force acting in the opposite direction of the deceleration. However, the normal force still balances the weight:
\[ N - mg = 0 \implies N = mg \]

4. **Conclusion:**
- Throughout all three phases of motion (acceleration, constant velocity, and deceleration), the normal force \( N \) exerted by the seat on the man remains equal to the gravitational force \( mg \).
- Thus, the force exerted by the seat on the man is:
\[ N = 490 \, \text{N} \]

### Final Answer:
The force exerted by the seat on the man is \( 490 \, \text{N} \).