Question

Let s = 100/(t2+12) be the position function of a particle moving along a coordinate line, where s is in feet and t is in seconds. (a) Find the maximum speed of the particle for t 0. If appropriate, leave your answer in radical form.

Answer 1

`v(t_(0))=(-200t_(0) )/((t_(0)^(2)+12)^(2)) ft/s`

Explanation:

Let's remember we could write the speed as a function of position taking the derivative whit respect to time.

`v(t)=(ds)/(dt)= (-200t)/((t^(2)+12)^(2))`

Now, evaluating the speed at t₀, we have:

`v(t_(0))=(-200t_(0))/((t_(0)^(2)+12)^(2)) ft/s`

It would be the maximun speed at that time.

Have a nice day!