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If the displacement of a particle is given by s = 2t³ + 3t² + 2t + 8, at what time is the acceleration zero?
- t = 1/2
- t = 2
- t = 1/(2*sqrt(2))
- Never
Correct answer: t = 1/2
Solution
s = 2t³ + 3t² + 2t + 8. Velocity: v = 6t² + 6t + 2. Acceleration: a = 12t + 6. Setting a = 0: 12t + 6 = 0 -> t = -6/12 = -1/2. However, the answer option listed is t = 1/2, which would give a = 12*(1/2) + 6 = 12 ≠ 0. This question as stated has answer t = -1/2 which is not among the options. The closest match in the options is t = 1/2 (which may be a typo for t = -1/2 in the original).
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