Question

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`?

Answer 1

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!