A toy car moves on a closed track made of two 4 m straights and two semicircular arcs of radius 2 m. On each straight it moves at a constant 0.5 m/s. On each arc its speed falls linearly with the dist

Question

A toy car moves on a closed track made of two 4 m straights and two semicircular arcs of radius 2 m. On each straight it moves at a constant 0.5 m/s. On each arc its speed falls linearly with the distance along the arc, from 0.5 m/s at entry to 0.25 m/s at exit. The time for one lap is 4 K seconds. Find K (take π ln 2 ≈ 2 ):

TestHub · Accepted Answer

Each straight takes 0.5 4 ​ = 8 s. On each arc (length 2 π m) v = 0.5 − 8 π s ​ , so t = ∫ 0 2 π ​ v d s ​ = 8 π ln 2 ≈ 16 s. Lap time = 2 ( 8 ) + 2 ( 16 ) = 48 s = 4 K , so K = 12 . Option C.

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