Question

an object of mass m is traveling at a constant speed v in a circle of radius r. In what direction is the acceleration of the object.

Answer 1

An object moving in a circular path with constant velocity is said to in uniform circular motion.

Acceleration is the rate of change of velocity. Change in velocity can be either in its magnitude or in its direction.

Here in uniform circular motion , the magnitude of velocity remains the same all the time. Then what results in acceleration is the change in direction of the velocity.

At every point on the circular path, the velocity is along the direction of the tangent at that point. Hence changing direction of velocity results in an acceleration in uniform circular motion.

Now the direction of this acceleration is towards the center of the circle. It provides the necessary centripetal force, that keep the mass in its circular path.