Answer to Question #167854 in Physics for clar

Question

Peter saw Lara Jean running on the school's track field. He accelerates from rest to 9.7 m/s within 23.8 s until he catches up with her. If Peter's mass is 74.02 kg, what is the average power (in hp) dissipated by Peter's body?

Answer 1

The average acceleration of Peter is:

$$a = \dfrac{v_2m/s-0m/s}{t} = \dfrac{v_2}{t}$$

where $v_2 = 9.7m/s$ is the final speed, $0m/s$ is the initial spee, and $t = 23.8s$ is the time.

Distance covered under this acceleration is:

$$d = \dfrac{at^2}{2} = \dfrac{v_2t}{2}$$

The average net force acted on Peter's body is (by second Newton's law):

$$F = ma$$

where $m = 74.02kg$ is Peter's mass. The average work done by Peter's body is:

$$A = Fd = ma\dfrac{v_2t}{2} = \dfrac{mv_2^2}{2}$$

Thus, the average power is given as (by definition):

$$P = \dfrac{A}{t} = \dfrac{mv^2_2}{2t}\\ P = \dfrac{74.02\cdot 9.7^2}{2\cdot 23.8} \approx 146.3W$$

Answer. 146.3 W.