# The position of an object moving along a line is given by p(t) = 7t - cos(( pi )/3t) + 2 . What is the speed of the object at t = 5 ?

##### 1 Answer
Jul 22, 2017

The speed is $= 6.09 m {s}^{-} 1$

#### Explanation:

We need

$\left(\cos x\right) ' = - \sin x$

The speed is the derivative of the position

$p \left(t\right) = 7 t - \cos \left(\frac{\pi}{3} t\right) + 2$

$v \left(t\right) = p ' \left(t\right) = 7 + \frac{1}{3} \pi \sin \left(\frac{\pi}{3} t\right)$

The speed at $t = 5$ is

$v \left(5\right) = 7 + \frac{1}{3} \pi \sin \left(\frac{5}{3} \pi\right)$

$= 7 + \frac{\pi}{3} \cdot - \frac{\sqrt{3}}{2}$

$= 6.09 m {s}^{-} 1$