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A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t − t³. How long would the particle travel before coming to rest?

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

Correct answer: 56m

Solution

To find when the particle comes to rest, we set its velocity to zero. Velocity is the derivative of displacement: v = dx/dt = 12 - 3t². Setting v = 0 gives t = 2s. Substituting t = 2s into x = 40 + 12t - t³, we find the distance traveled as x = 56m.

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