Particle Displacement, Velocity and Acceleration – Rankers Physics
Topic: Kinematics
Subtopic: Equations of Motion

Particle Displacement, Velocity and Acceleration

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

(1994)

3 m/s
42 m/s
-9 m/s
-15 m/s

Solution:

Concept: Kinematics equations involving differentiation.
Formula: Velocity \(v = \frac{ds}{dt}\) and acceleration \(a = \frac{dv}{dt}\).
Solution: Given \(s = t^3 - 6t^2 + 3t + 4\). Then \(v = 3t^2 - 12t + 3\) and \(a = 6t - 12\). Setting \(a=0\) gives \(t=2\text{ s}\). Substituting \(t=2\text{ s}\) into \(v\) gives \(v = 3(2)^2 - 12(2) + 3 = 12 - 24 + 3 = -9\text{ m/s}\).

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