# The position of an object moving along a line is given by p(t) = sin(2t- pi /4) +2 . What is the speed of the object at t = pi/2 ?

Apr 29, 2016

#### Answer:

$v \left(\frac{\pi}{2}\right) = - \sqrt{2}$

#### Explanation:

if p=f(t);

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

$v = \frac{d}{d t} \left(\sin \left(2 t - \frac{\pi}{4}\right) + 2\right)$

$v \left(t\right) = 2 \cdot \cos \left(2 t - \frac{\pi}{4}\right)$

$\text{for :} t = \frac{\pi}{2}$

$v \left(\frac{\pi}{2}\right) = 2 \cdot \cos \left(2 \cdot \frac{\pi}{2} - \frac{\pi}{4}\right)$

$v \left(\frac{\pi}{2}\right) = 2 \cdot \cos \left(\pi - \frac{\pi}{4}\right)$

$v \left(\frac{\pi}{2}\right) = 2 \cdot \cos \left(\frac{3 \pi}{4}\right)$

$\cos \left(\frac{3 \pi}{4}\right) = - \cos \left(\frac{\pi}{4}\right) = - \frac{\sqrt{2}}{2}$

$v \left(\frac{\pi}{2}\right) = - 2 \cdot \frac{\sqrt{2}}{2}$

$v \left(\frac{\pi}{2}\right) = - \sqrt{2}$