Question

The position of an object moving along a line is given by `p(t) = 2t - cos(( pi )/3t) + 2`. What is the speed of the object at `t = 5`?

Answer 1

`v(5) = 1.09` `"LT"^-1`

Explanation:

We're asked to find the speed of an object at `t = 5` (no units) with a given position equation,

To do this, we need to find the object's velocity as a function of time, by differentiating the position equation:

`v = (dp)/(dt) = d/(dt) [2t - cos(pi/3t) + 2] = color(red)(2 + pi/3sin(pi/3t)`

Now all we have to do is plug in `5` for `t` to find the velocity at `t = 5`:

`v(5) = 2 + pi/3sin(pi/3(5)) = color(blue)(1.09` `color(blue)("LT"^-1`

(The `"LT"^-1` term is the dimensional form of velocity; I used it here merely because no units were given.)