Answer in Physics for clar #167854
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?
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 = madfrac{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}\nP = dfrac{74.02cdot 9.7^2}{2cdot 23.8} approx 146.3W”
Answer. 146.3 W.
