# 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 ?

Jul 20, 2017

$v \left(5\right) = 1.09$ ${\text{LT}}^{-} 1$

#### 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 ${\text{LT}}^{-} 1$ term is the dimensional form of velocity; I used it here merely because no units were given.)