A Particle Moves Along A Straight Line Such That Its Displacement At Any Timet is Given By S = (t3 + 6t2 + 3t + 4)m. What Is The Velocity Of The Particle When Its Acceleration Is Zero?

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Question

A particle moves along a straight line such that its displacement at any timet is given by s = (t³ + 6t² + 3t + 4)m. What is the velocity of the particle when its acceleration is zero?

easy

Solution

Correct option is

– 9 m/s

As according to given problem,

S = t³ – 6t²+ 3t + 4

Instantaneous velocity

v = ds/dt = 3t² – 12t + 3 …(1)

and acceleration

So acceleration will be zero when 6t – 12 = 0, i.e., t = 2 sec. And the so velocity when acceleration is zero, i.e., at t = 2 sec from Eqn. (1), will be

v = 3 × 2² – 12 × 2 + 3 = – 9 m/s.