# The velocity of an object with a mass of 4 kg is given by v(t)= sin 3 t + cos 6 t . What is the impulse applied to the object at t= pi /3 ?

Mar 7, 2018

The impulse is $- 12$ Newton seconds.

#### Explanation:

We know that impulse is change in momentum. Momentum is given by $p = m v$, therefore impulse is given by $J = m \Delta v$

So we want to find the rate of change, or the derivative of the velocity function, and evaluate it at time $\frac{\pi}{3}$.

$v ' \left(t\right) = 3 \cos \left(3 t\right) - 6 \sin \left(6 t\right)$

$v ' \left(\frac{\pi}{3}\right) = 3 \cos \left(3 \left(\frac{\pi}{3}\right)\right) - 6 \sin \left(6 \left(\frac{\pi}{3}\right)\right)$

$v ' \left(\frac{\pi}{3}\right) = - 3$

Then we have

$J = m \Delta v$

$J = 4 \left(- 3\right)$

$J = - 12 k g \text{ } N s$

Hopefully this helps!