An object moves in a circular orbit starting from rest. the orbit has a radius of 10 m. it takes 10 revolutions to reach its final speed of 10 m/s. a) how far did it travel from rest to its final speed (in meters)?
b) if it accelerated at a constant rate, what was its tangential accelerate during that time?
c) once it reaches its final speed, what is its centripetal acceleration?

a)

b)

c)

Explanation:

a) If it did 10 revolutions, it returned to the original point, but it travelled 10 times the circunference , where r is the radius of the circle, so we have

b) The tangential component of this problem can be treated as a one dimensional problem, so the (tangential) acceleration needed to reach the final speed given starting from rest after traveling a distance d can be obtained using the equation for accelerated motion , so we have:

c) We use our values in the formula for centripetal acceleration given the tangential velocity and radius: