Respuesta :
Given that the speed is v = 32.1 m/s and time is t = 13.8 s.
Also, the diameter of the tire is d = 84.7 cm
We have to find the number of revolutions of the tire.
As the diameter is 84.7, so the radius will be
[tex]\begin{gathered} r=\frac{d}{2} \\ =\frac{84.7}{2} \\ =0.423\text{ m} \end{gathered}[/tex]The circumference of the circle will be
[tex]C=2\pi r[/tex]Substituting the values, the circumference will be
[tex]\begin{gathered} C=2\times3.14\times0.423 \\ =2.656\text{ m} \end{gathered}[/tex]The distance can be calculated using speed and time,
[tex]\begin{gathered} s=v\times t \\ =32.1\times13.8 \\ =442.98\text{ m} \end{gathered}[/tex]To find the number of revolutions, the formula will be
[tex]n\text{ =}\frac{\text{total distance}}{circumference}[/tex]Substituting the values, n will be
[tex]\begin{gathered} n=\frac{442.98}{2.656} \\ =166.78\text{ rev} \end{gathered}[/tex]