A simple pendulum is suspended from the roof of a car. The car starts from rest and accelerates uniformly on a straight horizontal road. If the pendulum hangs at an equilibrium angle of ⁻¹(0.5) with the vertical during the motion, what will be the velocity of the car after a time t ? (Assume g is the acceleration due to gravity)

Step-by-step solution

Let the acceleration of the car be a . In the non-inertial frame of the car, a pseudo force ma acts on the pendulum bob in the backward direction, while gravity mg acts downwards. At equilibrium, the angle made by the string with the vertical is given by: = ma mg = a g Given that = ⁻¹(0.5) , we have: a g = 0.5 a = 0.5g Using the first equation of motion for the car starting from rest ( u = 0 ): v = u + at v = 0 + (0.5g)t = 0.5gt Answer: 0.5gt