The velocity of an object with a mass of #3 kg# is given by #v(t)= sin 4 t + cos 4 t #. What is the impulse applied to the object at #t= pi /4 #?
From the basic theory of dynamics, if
Another result of Newton's second law is that, Change in momentum = Impulse
Assuming that the particle moves with the constant velocity
Now the momentum of the mass at
If the body/particle is stopped the final momentum is
This is equal to the impulse of the force.
The negative sign arises because the external force and hence it's impulse acts opposite to the particle's motion. If the particle's motion is assumed to be in the positive direction, the impulse is in the negative direction.
We have also assumed that the force stops the particle at the instant
I hope it helped.