Velocity at Zero Acceleration – Rankers Physics
Topic: Kinematics
Subtopic: Calculus Based Questions

Velocity at Zero Acceleration

A particle moves along a straight line such that its displacement at any time t is given by \(s = t^3 - 6t^2 + 3t + 4\). The velocity when its acceleration is zero is
\(2\text{ ms}^{-1}\)
\(12\text{ ms}^{-1}\)
\(-9\text{ ms}^{-1}\)
\(4\text{ ms}^{-1}\)

Solution:

Velocity \(v = 3t^2 - 12t + 3\) and acceleration \(a = 6t - 12\). Acceleration is zero at t = 2 s. Substituting \(t = 2\) in velocity equation gives \(v = 3(4) - 24 + 3 = -9 \text{ ms}^{-1}\).

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