# The velocity of an object with a mass of 8 kg is given by v(t)= sin 4 t+ cos 13 t . What is the impulse applied to the object at t= ( 3 pi)/ 4 ?

Feb 9, 2016

$\overline{J} = 5 , 656 \text{ N.s}$

#### Explanation:

$\overline{J} = \int F \left(t\right) \cdot d t$
$F = m \cdot a = m \cdot \frac{d v}{d t}$
$\overline{J} = \int m \cdot \frac{d v}{d t} \cdot d t$
$\overline{J} = m \int d v$
$d v = \left(4 \cos 4 t - 13 \sin 13 t\right) \cdot d t$
$\overline{J} = m \int \left(4 \cos 4 t - 13 \sin 13 t\right) \cdot d t$
$\overline{J} = m \left(\sin 4 t + \cos 13 t\right)$
$\overline{J} = 8 \left(\sin 4 \cdot 3 \frac{\pi}{4} + \cos 13 \cdot 3 \frac{\pi}{4}\right)$
$\overline{J} = 8 \cdot \left(0 + 0 , 707\right)$
$\overline{J} = 8 \cdot 0 , 707$
$\overline{J} = 5 , 656 \text{ N.s}$