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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.

Respuesta :

Answer:

[tex]t=5.72\ s[/tex]

Explanation:

Given:

the displacement as the function of time:

[tex]s=2t^3-3t^2-63t[/tex]

here time is in seconds and the displacement in meters.

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

[tex]v=\frac{d}{dt}(s) \\v=6t^2-6t-63[/tex]

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

[tex]99=6t^2-6t-63[/tex]

[tex]6t^2-6t-162=0[/tex]

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

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