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A particle travels on a straight line OX. Its displacement x, in metres, from O at time t seconds is given by x = 40 + 12t - t³. What distance does the particle cover before it comes to rest?

1. 40 m
2. 56 m
3. 16 m
4. 24 m

Correct answer: 16 m

Solution

x = 40 + 12t - t^3, so v = dx/dt = 12 - 3t^2 = 0 gives t = 2 s. Velocity stays positive for 0<t<2, so the particle moves monotonically; distance covered = x(2) - x(0) = (40 + 24 - 8) - 40 = 16 m.

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