# The velocity of an object with a mass of 3 kg is given by v(t)= sin 2 t + cos 9 t . What is the impulse applied to the object at t= ( 7 pi)/ 12 ?

Dec 19, 2015

I found $25.3 N s$ but check my method....

#### Explanation:

I would use the definition of impulse but in this case at an instant:
$\text{Impulse} = F \cdot t$
where:
$F =$force
$t =$time
I try to rearrange the above expression as:

$\text{Impulse} = F \cdot t = m a \cdot t$

Now, to find the acceleration I find the slope of the function describing your velocity and evaluate it at the given instant.
So:

$v ' \left(t\right) = a \left(t\right) = 2 \cos \left(2 t\right) - 9 \sin \left(9 t\right)$

at $t = \frac{7}{12} \pi$

$a \left(\frac{7}{12} \pi\right) = 2 \cos \left(2 \cdot \frac{7}{12} \pi\right) - 9 \sin \left(9 \cdot \frac{7}{12} \pi\right) = 4.6 \frac{m}{s} ^ 2$

So the impulse:

$\text{Impulse} = F \cdot t = m a \cdot t = 3 \cdot 4.6 \cdot \frac{7}{12} \pi = 25.3 N s$