A car of mass M travels on a horizontal circular path of radius r . At a given instant, its speed is v and is increasing at a rate a .

Step-by-step solution

The car moving on a horizontal circular path with an increasing speed has two components of acceleration: Tangential acceleration, a_t = a Centripetal acceleration, a_c = v^2 r The net acceleration of the car is given by a_ net = a_t^2 + a_c^2 = a^2 + ( v^2 r )^2 . Since there is a tangential component, the net acceleration is not directed towards the centre of the path. The required force is provided by the frictional force f between the car and the ground. Thus, f = M a_ net = M a^2 + ( v^2 r )^2 . Since a > 0 ,