Emery Hill

2023-02-28

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 ?

Valentino Sloan

Centripetal acceleration ${a}_{c}$ the following is stated
${a}_{c}=R{\omega }^{2}=\frac{{v}^{2}}{R}$
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
Comparing the size of two and putting in a value $R$ we obtain
$\frac{{v}^{2}}{400}=0.500$

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