A driver enters a circular freeway entrance ramp of constant radius
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A driver enters a circular freeway entrance ramp of constant radius. Three distinct stages of motion are considered:
• Stage I: The car moves at a steady speed while entering the curve.
• Stage II: While on the same curve, the driver presses the accelerator, and the car’s speed increases.
• Stage III: Still on the same curve, the driver releases the accelerator so that the car’s speed decreases.
(a) For each stage, describe the direction of the car’s net acceleration vector relative to the center of curvature and the direction of motion.
(b) Compare the magnitudes of the radial and tangential components of acceleration in each stage, and explain your reasoning.
(c) Sketch qualitatively how the magnitude of the net acceleration might vary with time as the car progresses through Stages I, II, and III.
(d) In Stage II, explain how the angle between the net acceleration vector and the inward radial direction changes as the car speeds up, and relate this to the changing magnitudes of the acceleration components.