D

Step 1: Analyze the forces acting on the boy in the elevator.
The forces acting on the boy are his weight and the normal force exerted by the elevator floor on his feet.
The weight of the boy is given by:
Weight (W) = mass (m) × gravitational acceleration (g)

Weight (W) = 40 kg × 9.8 m/s² = 392 N

Step 2: Evaluate the scenarios:
1. **Elevator stands still:**
The boy feels the full weight.
Normal Force (N) = Weight = 392 N

2. **Moves downward at a constant velocity (4 m/s):**
There is no acceleration, thus:
Normal Force (N) = Weight = 392 N

3. **Accelerates downward (4 m/s²):**
The effective weight is reduced by the acceleration of the elevator:
Net Force (N) = Weight - (mass × acceleration)
N = 392 N - (40 kg × 4 m/s²) = 392 N - 160 N = 232 N

4. **Accelerates upward (4 m/s²):**
The effective weight increases as the elevator accelerates upward:
Net Force (N) = Weight + (mass × acceleration)
N = 392 N + (40 kg × 4 m/s²) = 392 N + 160 N = 552 N

Step 3: Compare the normal forces from the different scenarios. The force felt by the feet of the boy is greatest when the elevator accelerates upward (552 N).

Therefore, the correct answer is option D.