# 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 #?

##### 1 Answer

Mar 7, 2018

#### Answer:

The impulse is

#### Explanation:

We know that impulse is change in momentum. Momentum is given by

So we want to find the rate of change, or the derivative of the velocity function, and evaluate it at time

#v'(t) = 3cos(3t) - 6sin(6t)#

#v'(pi/3) = 3cos(3(pi/3)) - 6sin(6(pi/3))#

#v'(pi/3) = -3#

Then we have

#J = mDelta v#

#J= 4(-3)#

#J = -12 kg" "Ns#

Hopefully this helps!