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A car begins from rest and speeds up with constant acceleration f over a distance S. It then moves with that attained speed for a time t, and finally slows down with constant deceleration f/2 until it stops. If the entire journey covers a total distance of 15S, what is the value of S?

1. S = 1/6 ft²
2. S = ft
3. S = 1/4 ft²
4. S = 1/72 ft²

Correct answer: S = 1/72 ft²

Solution

v^2 = 2fS so accel covers S; deceleration at f/2 covers v^2/f = 2S; cruise covers vt. Total = S + vt + 2S = 15S gives vt = 12S. Then t = 12S/sqrt(2fS) -> t^2 = 72S/f, so S = f t^2 / 72.

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