Answer to Question #168618 in Physics for Phyroe

Question

A runner travels 1.5 laps around a circular track in a time of 50 s. The diameter of truck is 40 m and its circumference is 126 m. Find (a) the average speed of the runner and (b) the magnitude of the runner averwge's velocity. Be careful here: average speed depends on the distance traveled, whereas average depends on the displacement at the end of the particular journey.

Answer 1

a) The distance travelled by the runner (1.5 of the circle with the circumference 126 m) is:

$$l = 1.5\times 126m = 189m$$

Since the time is $t = 50s$, then the average speed is:

$$speed = \dfrac{l}{t} = \dfrac{189m}{50s} = 3.78 m/s$$

b) The displacement of the runner at the end of the jorney is equal to the diameter of the circle, since she completed 1.5 laps. The diameter is $d = 40m$. Thus, the average velocity is:

$$velocity = \dfrac{d}{t} = \dfrac{40m}{50s} = 0.8m/s$$

Answer. a) 3.78 m/s, b) 0.8 m/s.