# The position of an object moving along a line is given by p(t) = 2t - cos(( pi )/6t) . What is the speed of the object at t = 7 ?

Jul 15, 2017

$v = 1.74$ ${\text{LT}}^{-} 1$

#### Explanation:

We're asked to find the speed of an object moving in one dimension at a given time, given its position-time equation.

We therefore need to find the velocity of the object as a function of time, by differentiating the position equation:

$v \left(t\right) = \frac{d}{\mathrm{dt}} \left[2 t - \cos \left(\frac{\pi}{6} t\right)\right] = 2 + \frac{\pi}{6} \sin \left(\frac{\pi}{6} t\right)$

At time $t = 7$ (no units here), we have

v(7) = 2 + pi/6sin(pi/6(7)) = color(red)(1.74 color(red)("LT"^-1

(The term ${\text{LT}}^{-} 1$ is the dimensional form of the units for velocity (${\text{length"xx"time}}^{-} 1$) . I included it here because no units were given.