Answer to Question #253378 in Mechanics | Relativity for taeh

Question #253378

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.


1
Expert's answer
2021-10-19T15:10:31-0400

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


vavg=Total distanceTotal elapsed time=2.5×Ct,v_{avg}=\dfrac{Total\ distance}{Total\ elapsed\ time}=\dfrac{2.5\times C}{t},vavg=2.5×126 m2.5 min×60 s1 min=2.1 ms.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:


vavg=DisplacementTotal time.\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:


vavg=40 m2.5 min×60 s1 min=0.27 ms.\vec{v}_{avg}=\dfrac{40\ m}{2.5\ min\times\dfrac{60\ s}{1\ min}}=0.27\ \dfrac{m}{s}.

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