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

`t=5.72\ s`

Step-by-step 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=(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.