Question

The position of an object moving along a line is given by `p(t) = 3t - tcos(( pi )/4t)`. What is the speed of the object at `t = 7`?

Answer 1

`3 -sqrt(2)/2 - (7sqrt(2)pi)/8`

Explanation:

You're looking for the velocity of the object. You can find the velocity `v(t)` like this:
`v(t) = p'(t)`
Basically, we have to find `v(7)` or `p'(7)`.
Finding the derivative of `p(t)`, we have:
`p'(t) = v(t) = 3 - cos(pi/4t) + pi/4tsin(pi/4t)` (if you don't know how I did this, I used power rule and product rule)
Now that we know `v(t) = 3 - cos(pi/4t) + pi/4tsin(pi/4t)`, let's find `v(7)`.
`v(7) = 3 - cos(pi/4 * 7) + pi/4 * 7sin(pi/4 * 7)`
`=3 - cos((7pi)/4) + (7pi)/4 * sin((7pi)/4)`
`=3 - sqrt(2)/2 - (7pi)/4 * sqrt(2)/2`
`v(7) =3 -sqrt(2)/2 - (7sqrt(2)pi)/8`