Question

A car drives on a circular track with a constant speed of 84 m/s. The track has a radius of 225 m. What is the centripetal acceleration of the car? What is the acceleration of the car measured in g? What speed would give the car an acceleration of 9.8 m/s2?

Answer 1

To make Edufirst's answer easier to read:

Centripetal acceleration of the car: 31.36 m/s

Acceleration of the car measured in g: 3.2 g's

Speed that would give the car an acceleration of 9.8 m/s: 47 m/s

Answer 2

Data:

a) v = 84 m/s

r = 225 m

Ac =?

b) Ac = 9.8 m/s^2

v = ?

Formula: Ac = v^2 / r

Solution

a) Ac = (84 m/s)^2 / (225 m) = 31.36 m/s^2

To measure it in terms of g, divide by g = 9.8 m/s^2

=> Ac = 31.36 m/s^2 / [ 9.8 m/s^2 / g] = 3.2 g

Answer: Ac = 3.2 g

b) Ac = 9.8 m/s^2

v^2 = Ac * r = 9.8 m/s^2 * 225 m = 2,205 m^2 / s^2

=. v = 46.96 m/s ≈ 47 m/s

Answer: 47 m/s