# 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 = 5 ?

Mar 15, 2017

$v \left(5\right) = 0.931$

#### Explanation:

$\text{We need to find the time derivative of the function.}$

$v \left(t\right) = \frac{d}{d t} p \left(t\right)$

v(t)=d/(d t) (3t-t cos(pi/4 t)

$\text{We get;}$

$v \left(t\right) = 3 - 1 \cdot \cos \left(\frac{\pi}{4} t\right) + t \cdot \frac{\pi}{4} \sin \left(\frac{\pi}{4} t\right)$

$\text{for t=5}$

$v \left(5\right) = 3 - \cos \left(\frac{5 \pi}{4}\right) + 5 \cdot \frac{\pi}{4} \sin \left(\frac{5 \pi}{4}\right)$

$\cos \left(\frac{5 \pi}{4}\right) = - \frac{\sqrt{2}}{2} = - 0.707$

$\sin \left(\frac{5 \pi}{4}\right) = - \frac{\sqrt{2}}{2} = - 0.707$

$v \left(5\right) = 3 + 0.707 - 5 \cdot \frac{\pi}{4} \cdot 0.707$

$v \left(5\right) = 3.707 - \frac{3.535 \cdot \pi}{4}$

$v \left(5\right) = 3.707 - 2.776$

$v \left(5\right) = 0.931$