# The velocity of an object with a mass of 3 kg is given by v(t)= sin 6 t + cos 9 t . What is the impulse applied to the object at t= ( 7 pi)/ 12 ?

Feb 18, 2016

$F \cdot t = 0 , 7642 N . s$

#### Explanation:

$\int F . d t = \int m \cdot d v$
$F \cdot t = m \int d v$
$F \cdot t = m \cdot \int \left(\sin 6 t + \cos 9 t\right) d t$
$F \cdot t = m \cdot \left[- \frac{1}{6} \cdot \cos 6 t + \frac{1}{9} \cdot \sin 9 t\right] + C$
F(0)=1 ; C=1
$F \cdot t = m \cdot \left[- \frac{1}{6} \cdot \cos 6 t + \frac{1}{9} \cdot \sin 9 t\right] + 1$
$t = \frac{7 \pi}{12}$
$F \cdot t = 3 \left[- \frac{1}{6} \cdot \cos 42 \frac{\pi}{12} + \frac{1}{9} \cdot \sin 63 \frac{\pi}{12}\right] + 1$
$F \cdot t = 3 \left[- \frac{1}{6} \cdot 0 - \frac{1}{9} \cdot 0 , 707\right] + 1$
$F \cdot t = 3 \left(- 0 , 0786\right) + 1$
$F \cdot t = - 0 , 2358 + 1$
$F \cdot t = 0 , 7642 N . s$