Four identical cars—P, Q, R, and S—move around four different circular test tracks. All four cars complete exactly one revolution every 18 s, but each track has a different radius:
• P: 30 m • Q: 45 m • R: 60 m • S: 75 m
a) Derive an algebraic relationship between the magnitude of centripetal acceleration and track radius for any car that completes one revolution in a fixed time interval T=18s.
b) Using your expression from part (a), calculate the centripetal acceleration of each car. Provide answers in m s⁻² with an appropriate number of significant figures.
c) Rank the cars from greatest to least centripetal acceleration and justify the ranking without re-calculating numerical values.
d) Suppose car P’s driver wants to double the magnitude of the centripetal acceleration without shortening the period. Determine the new radius required and explain your reasoning.