Question

Which has the greater centripetal acceleration, a car with a speed of 15.0 m/s along a circular track of radius 100.0 m or a car with a speed of 12.0 m/s along a circular track of radius 75.0 m?

a) Car with 15.0 m/s
b) Car with 12.0 m/s
c) Both have the same

Answer 1

Comparing the given formula for centripetal acceleration, the car with a speed of 15.0 m/s has greater centripetal acceleration of 2.25 m/s² compared to the car with a speed of 12.0 m/s, which has centripetal acceleration of 1.92 m/s².

Step-by-step explanation:

The centripetal acceleration of an object moving in a circle at speed v and radius r is given by the formula ac = v2 / r, where ac is the centripetal acceleration, v is the speed, and r is the radius of the circle.

To determine which car has greater centripetal acceleration, we'll use the formula above.

• For the car with a speed of 15.0 m/s and a radius of 100.0 m, ac = (15.0 m/s)2 / 100.0 m = 2.25 m/s2.
• For the car with a speed of 12.0 m/s and a radius of 75.0 m, ac = (12.0 m/s)2 / 75.0 m = 1.92 m/s2.

The car with a speed of 15.0 m/s has a greater centripetal acceleration than the car with a speed of 12.0 m/s.