Question

A particle moves along a straight line such that its displacement at any time t is given by:
S= t^3 -6t²+3t+4 mts.
The velocity when the acceleration is zero is:

Answer 1

Answer:

-9m/s

Explanation:

Using differentiation

Answer 2

Given,

Displacement of the particle S=t³-6t²+3t+4

To Find,

Velocity when the acceleration is zero.

Solution,

Here, S=t³-6t²+3t+4

We know, V=ds/dt

So, differentiating the expression we get,

V=d(t³-6t²+3t+4)/dt

  =3t²-12t+3

And acceleration, a=dV/dt

So, we have to differentiate it again,

So, a=d(3t²-12t+3)/dt

      =6t-12

So, it has asked for when acceleration is 0,

Means, 6t-12=0

          ⇒t=2s

Then the velocity will be at t =2s,

V=3t²-12t+3

  =3×2²-12ײ+3

  =3×4-24+3

  =12-24+3

  =12-21

  =-9

Hence, the velocity when the acceleration is zero is -9m/s