A

Step 1: Calculate the weight of the elevator.
The weight (W) is given by the formula:
W = mass \times g
W = 500 \, \text{kg} \times 10 \, \text{m/s}^2 = 5000 \, \text{N}.

Step 2: Since the elevator moves at constant velocity, the tension in the cable must equal the weight (5000 N).

Step 3: Calculate the power required to lift the elevator at this constant velocity.
Power (P) is given by the formula:
P = force \times velocity
P = 5000 \, \text{N} \times 0.4 \, \text{m/s} = 2000 \, \text{W}.

Step 4: Convert power in watts to horsepower.
Since 1 hp = 750 watts,
Power in hp = \frac{2000 \, \text{W}}{750 \, \text{W/hp}} = \frac{2000}{750} \approx 2.67 \, \text{hp}.

Step 5: The minimum horsepower of the motor should be rounded up since it must be sufficient to lift the elevator. Therefore, the minimum horsepower required is approximately 3 hp.