Question

Dave runs up a flight of stairs with a total change in energy ΔE_D. Kim exerts double the amount of energy in half the time. How does Dave's power output, P_D, compare with Kim's power output, P_K?

A) P_D is half of P_K.
B) P_D is equal to P_K.
C) P_D is double P_K.
D) P_D is four times P_K.

Answer 1

Dave's power output, PD, is one fourth of Kim's power output, PK, because Kim does double the work in half the time, resulting in her power output being four times greater than Dave's.

Step-by-step explanation:

We are asked to compare Dave's power output, PD, with Kim's power output, PK, given that Dave runs up a flight of stairs with a total change in energy ΔED and Kim exerts double the amount of energy in half the time.

Power is defined as the work done over time (P = W/t). Since Kim does double the work in half the time, she makes four times the power output compared to Dave. This is because when you double the numerator (work) and halve the denominator (time) in the power formula, the resulting power is quadrupled.

Therefore, the correct answer is D) PD is four times PK.