The position function of a particle is given by s=2t3−3t2−63t, t⩾0.s=2t3−3t2−63t, t⩾0. where ss is measured in meters and tt in seconds. Find all values of t⩾0t⩾0 for which the particle is moving at a velocity of 99 ms.

Explanation:

Given:

the displacement as the function of time:

here time is in seconds and the displacement in meters.

Now we differentiate this eq. of displacement to get the equation of velocity:

According to given the velocity is at some time:

&  is the only time  for (t>=0) instances when the particle will have a velocity of but in the opposite direction.