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A particle moves along a straight line such that its displacement at any time t is given by s = (t³ − 6t² + 3t + 4) metres. The velocity when the acceleration is zero is:

1. 3 m/s
2. −12 m/s
3. 42 m/s
4. −9 m/s

Correct answer: −9 m/s

Solution

To find the velocity when acceleration is zero, first calculate acceleration by differentiating the displacement equation twice: a = d²s/dt² = 6t - 12. Set a = 0 to get t = 2 s. Then, find velocity by differentiating displacement once: v = ds/dt = 3t² - 12t + 3. Substituting t = 2, v = 3(2)² - 12(2) + 3 = -9 m/s.

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