Final answer:
To find the power needed to lift a 4.00-kg box vertically at a constant speed, calculate the weight and multiply by the velocity. The correct calculation results in a power of approximately 196 W, which indicates a discrepancy with the given multiple-choice options; the closest option is 200 W (a).
Step-by-step explanation:
The student's question pertains to calculating the power required to lift an object vertically at a constant speed, which is a common topic in physics, specifically in the area of work and energy. Power is the rate at which work is done and can be calculated using the formula P = Fv, where P is power, F is the force applied, and v is the velocity. Since the box is being raised at a constant velocity, the force is equal to the gravitational force, which is the weight of the object (mass times gravity).
The weight (F) of the 4.00-kg box is given by F = mg, where m is the mass (4.00 kg) and g is the acceleration due to gravity (9.80 m/s2), thus F = (4.00 kg)(9.80 m/s2) = 39.2 N. The power (P) needed to lift the box at constant velocity (v = 5.00 m/s) can be calculated using P = Fv:
P = (39.2 N)(5.00 m/s) = 196 W.
However, since 196 W is not one of the multiple-choice options provided and due to rounding or precision issues in the available answers, we consider the closest option, which is (a) 200 W, acknowledging a potential discrepancy with the given choices.