Question

A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. Calculate (a) the average speed and (b) the average velocity, in m/s. Note: 1 mile = 1609 m.

Answer 1

$\large\displaystyle\text{ \begin{gathered}\sf \huge \bf{\underline{Data:}} \end{gathered} }$

• $\large\displaystyle\begin{gathered}\sf 1\ mile = 1609.34 \ m \end{gathered}$

• $\large\displaystyle\begin{gathered}\sf 1/4 \ mile = 402.33 \ m \end{gathered}$

                           $\large\displaystyle\text{ \begin{gathered}\sf 12.5 \not{min}*\frac{60 \ s}{1\not{min}}=750 \ s \end{gathered} }$

                   $\large\displaystyle\begin{gathered}\sf \bf{A) \ Calculate \ the \ average \ speed: } \end{gathered}$

                         $\large\displaystyle\begin{gathered}\sf 402.33 \ m*8 \ laps = 3218.64 \ m \end{gathered}$

                         $\large\displaystyle\begin{gathered}\sf d=3218.64 \ m \end{gathered}$

                         $\large\displaystyle\begin{gathered}\sf t=750 \ s \end{gathered}$

                         $\large\displaystyle\begin{gathered}\sf V=\frac{d}{t} \ \ \ \ \ \ V= \frac{3218.64 \ m }{750 \ s} \end{gathered}\\\\\\\large\displaystyle\begin{gathered}\sf V=4.29 \ m/s \end{gathered}$

                  $\large\displaystyle\begin{gathered}\sf \bf{B) \ Calculate \ the \ average \ speed \ in \ m/s} \end{gathered}$

                          $\large\displaystyle\begin{gathered}\sf V=402.33 \ m \end{gathered}$  

                          $\large\displaystyle\begin{gathered}\sf t=750 \ s \end{gathered}$

                          $\large\displaystyle\begin{gathered}\sf V=\frac{D}{T} \ \ \ \ \ V=\frac{402.33 \ m}{750 \ s} \end{gathered}\\\\\\\large\displaystyle\begin{gathered}\sf V= 0.53 \ m/s \end{gathered}$