Question

The acceleration of an object moving in a circle of 5 m radius at constant speed is 45 m/s2. What is it’s speed in m/s?

Answer 1

Given

radius of the circle r = 5 m, acceleration of the object is a = 45 m/s2

moving with constant speed v = ?

we know that , when an object is moving with constant speed on the circumferance of a circle of radius R then it is called the uniform circular motion , as along as it is in circular motion a force will act towards the center called the Centripetal force

we know that the cetripetal force is F = mv^2/r

and the Centripetal acceleration is also known as radial acceleration as it is along the radius of the circle

given as a_rad = v^2/R ==> v^2 = a_rad*R ==> v = sqrt(a_rad*R)

substituting the values  

v = sqrt(45*5) m/s

v = 15 m/s

so the speed of the object is v = 15 m/s