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\text{$\begin{gathered}\sf 1\ mile = 1609.34 \ m \end{gathered}$}`

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

`\large\displaystyle\text{$\begin{gathered}\sf 12.5 \\ot{min}*\frac{60 \ s}{1\\ot{min}}=750 \ s \end{gathered}$}`

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

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

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

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

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

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

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

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

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