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.
Answer in units of m/s.
Is it V^2/r.
The radial acceleration of the car moving in a circular path is given by:
Radial acceleration = (v^2)/r
v = tangential speed (velocity)
r = radius of circular path = 430 m (Given)
It is given:
Tangential acceleration = 0.3 m/s^2
Radial acceleration = Tangential acceleration:
==> (v^2)/r = 0.3
==> (v^2)/430 = 0.3
==> v^2 = 0.3*430 = 129
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.)