A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

Apr 9, 2018

Centripetal acceleration ${a}_{c}$ is given by the expression

${a}_{c} = R {\omega}^{2} = {v}^{2} / R$
where $v$ is linear velocity of the object, $\omega$ is its angular velocity and $R$ is the radius of the circle in which object moves.

Tangential acceleration ${a}_{t}$ is given to be $= 0.500 \setminus m {s}^{-} 2$

Equating the magnitudes of two and inserting value of $R$ we get

${v}^{2} / 400 = 0.500$
$\implies v = \sqrt{0.500 \times 400} = \sqrt{200} = 14.142 \setminus m {s}^{-} 1$