Question

A race car moving along a circular track has a centripetal acceleration of 12 m/s. If

the distance between the car and the center of the track is 40 m, what is the speed
of the car?

Answer 1

The speed of the car is 21.91 m/s

Explanation:

Centripetal Acceleration

It's the acceleration experienced by an object in a uniform circular motion.

It always points toward the center of rotation and is perpendicular to the linear velocity v.

The magnitude of the centripetal acceleration is:

`\displaystyle a_c=(v^2)/(r)`

Where r is the radius of rotation.

The race car has a centripetal acceleration of
`a_c=12 m/s^2` and the radius of rotation is r=40 m.

We can calculate the speed of the car by solving the above equation for v:

`v=√(a_c\cdot r)`

`v=√(12\cdot 40)`

`v=√(480)`

`v=21.91\ m/s`

The speed of the car is 21.91 m/s