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The displacement of a particle varies with time (t) as: s = at² − bt³. The acceleration of the particle will be zero at time t equal to:

1. a/b
2. 3b/2a
3. 3b/a
4. 2a/3b

Correct answer: 2a/3b

Solution

To find when acceleration is zero, we first calculate velocity by differentiating displacement: v = ds/dt = 2at - 3bt². Then, acceleration is a = dv/dt = 2a - 6bt. Setting a = 0 gives 2a = 6bt, or t = 2a/3b.

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