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 #-12# Newton seconds.

Explanation:

We know that impulse is change in momentum. Momentum is given by #p =mv#, therefore impulse is given by #J = mDeltav#

So we want to find the rate of change, or the derivative of the velocity function, and evaluate it at time #pi/3#.

#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!