Question

A new car is tested on a 300-m-diameter track.

A) If the car speeds up at a steady 1.5 m/s^2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Answer 1

Radius of a track, r = d/2 = 150 m

Tangential acceleration of the car which will be given as -

a_t = 1.5 m/s²

Centripetal acceleration of the car which will be given by -

a_c = v² / r

We know that, the magnitude of its centripetal acceleration equals to the tangential acceleration.

Then, we have

a_t = v² / r   v = a_t . r

v = [(1.5 m/s²) (150 m)]

v = 225 m²/s²

v = 15 m/s

Time taken by the car after starting point which will be given as -

t = v / a_t

t = [(15 m/s) / (1.5 m/s²)]

t = 10 sec