PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
A car of mass 1 200 kg moves on a horizontal, circular test track of radius 200 m. Starting from rest at point A, the driver depresses the accelerator so that the car experiences a constant tangential acceleration of 1.2 m s⁻² while staying on the track.
(a) Derive an expression for the car’s speed v(t) as a function of time t measured from the instant it leaves point A.
(b) Using your result from part (a), obtain an expression for the magnitude of the radial component of acceleration a_r(t) as a function of time.
(c) Write an expression for the magnitude of the net acceleration a_net(t) as a function of time.
(d) Determine the time t_eq at which the radial and tangential components of acceleration have equal magnitudes.
(e) At the instant found in part (d), calculate the angle between the net acceleration vector and the inward radial direction, and state whether the net acceleration points more toward the center or more along the tangent at that instant.