Question

A new car is tested on a 300-mm-diameter track. If the car speeds up at a steady 1.2 m/s2m/s2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Answer #1

Diameter of the track = D = 300 m

Radius of the track = R = D/2 = 300/2 = 150 m

Acceleration of the car = a = 1.2 m/s^{2}

Angular acceleration of the car =

Time period when the centripetal acceleration of the car is equal to the tangential acceleration of the car = T

Angular speed of the car at this moment =

Centripetal acceleration of the car = a_{c}

Tangential acceleration of the car = a_{t}

a_{t} = a

The magnitude of the centripetal acceleration and the tangential acceleration are equal therefore,

T = 11.18 sec

**Time period when the centripetal acceleration of the car
is equal to the tangential acceleration of the car = 11.18
sec**

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