Answer to Question #253378 in Mechanics | Relativity for taeh

Question

A man makes 2.5 laps around a circular lap 2.5 minutes. The circumference of the track is 126 m while its diameter is 40 m. Compute the man’s (a) average speed, and (b) average velocity.

Answer 1

(a) By the definition of the average speed we have:

$$v_{avg}=\dfrac{Total\ distance}{Total\ elapsed\ time}=\dfrac{2.5\times C}{t},$$ $$v_{avg}=\dfrac{2.5\times126\ m}{2.5\ min\times\dfrac{60\ s}{1\ min}}=2.1\ \dfrac{m}{s}.$$

(b) By the definition of the average velocity we have:

$$\vec{v}_{avg}=\dfrac{Displacement}{Total\ time}.$$

In our case displacement is 0.5 lap which is equal to the diameter of the track. Therefore, we get:

$$\vec{v}_{avg}=\dfrac{40\ m}{2.5\ min\times\dfrac{60\ s}{1\ min}}=0.27\ \dfrac{m}{s}.$$