Question

A new car is tested on a 230-m-diameter track. If the car speeds up at a steady 1.6 m/s2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration

Answer 1

The centripetal acceleration (a) is given by:

a = v^2 / r

v^2 = ar

where v is the tangential velocity and r is the radius of the circular path.

we know:

a = 1.6 m/s^2

r = (230 / 2) = 115 m/s

v^2 = 1.6 x 115 = 184 m^2/s^2

v = 13.565 m/s

So now we need to calculate how long it takes a car, starting from rest, to reach a velocity of 13.565 m/s when it is

accelerating at 1.6 m/s^2

v = u + at

v = 13.565 m/s

u = 0 m/s is the initial velocity = 0

a = 1.6 m/s^2

t = 13.565 / 1.6 = 8.4779 s