Question

A test car moves at a constant speed around a circular track. If the car is 48.2 m from the tracks center and has a centripetal acceleration of 8.05m/s^2 what is the cars velocity?

Answer 1

Given data:

* The radius of the circular motion of the car is r = 48.2 m.

* The acceleration of the car is,

`a=8.05ms^(-2)`

Solution:

The centripetal force acting on the car in terms of the acceleration is,

`F=ma`

The centripetal force acting on the car in terms of velocity and radius is,

`F=(mv^2)/(r)`

As the force acting on the car is the same in either case, thus,

`\begin{gathered} (mv^2)/(r)=ma \\ (v^2)/(r)=a \\ v^2=ra \\ v=\sqrt[]{ra} \end{gathered}`

Substituting the known values,

`\begin{gathered} v=\sqrt[]{48.2*8.05} \\ v=19.7\text{ m/s} \end{gathered}`

Thus, the velocity of the car is 19.7 meters per second.