# Circular MotionA race car starts from rest on a circular trackof radius 430 m. Its speed increases at theconstant rate of 0.3 m/s2. At the point wherethe magnitudes of the radial and...

Circular Motion

A race car starts from rest on a circular track
of radius 430 m. Its speed increases at the
constant rate of 0.3 m/s2. At the point where
the magnitudes of the radial and tangential
accelerations are equal, determine the speed
of the race car.

Is it V^2/r.

krishna-agrawala | Student

The radial acceleration of the car moving in a circular path is given by:

Where:

v = tangential speed (velocity)

r = radius of circular path = 430 m (Given)

It is given:

Tangential acceleration = 0.3 m/s^2

When:

==> (v^2)/r = 0.3

==> (v^2)/430 = 0.3

==> v^2 = 0.3*430 = 129

Therefore:

v = 129^(1/2) = 11.3578 m/s

Speed of the car = 11.3578 m/s

(Here you can see that the expression V^2/r given in the question refers to the radial acceleration, although the way I have expressed it is slightly different.)