Question

A particle’s centripetal acceleration is aC=4.0 m/s² at t = 0 s where it is on the x-axis and moving counterclockwise in the xy plane. It is executing uniform circular motion about an axis at a distance of 5.0 m. What is its velocity at t = 10 s?

a) 20 m/s
b) 30 m/s
c) 40 m/s
d) 50 m/s

Answer 1

The velocity of the particle at t = 10 s is 10 m/s.

Step-by-step explanation:

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of rotation and has a magnitude of v² / r, where v is the linear velocity of the object and r is the radius of the circle.

In this question, we are given that the centripetal acceleration (ac) is 4.0 m/s² at t = 0s and the object is moving counterclockwise on the x-axis in the xy plane. The object is executing uniform circular motion about an axis at a distance of 5.0 m.

To find the velocity at t = 10 s, we can use the formula for centripetal acceleration: ac = v² / r. Rearranging the formula, we get v = sqrt(ac * r). Plugging in the values, we get v = sqrt(4.0 * 5.0) = 10 m/s at t = 10 s.