Question

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.

Answer 1

Answer:

$t=5.72\ s$

Explanation:

Given:

the displacement as the function of time:

$s=2t^3-3t^2-63t$

here time is in seconds and the displacement in meters.

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

$v=\frac{d}{dt}(s) \\v=6t^2-6t-63$

According to given the velocity is $99\ m.s^{-1}$ at some time:

$99=6t^2-6t-63$

$6t^2-6t-162=0$

$t=5.72\ s$ &  is the only time  for (t>=0) instances when the particle will have a velocity of $99\ m.s^{-1}$ but in the opposite direction.