Question

The velocity of an object with a mass of `3 kg` is given by `v(t)= sin 2 t + cos 9 t`. What is the impulse applied to the object at `t= ( 7 pi)/ 12`?

Answer 1

I found `25.3Ns` but check my method....

Explanation:

I would use the definition of impulse but in this case at an instant:
`"Impulse"=F*t`
where:
`F=`force
`t=`time
I try to rearrange the above expression as:

`"Impulse"=F*t=ma*t`

Now, to find the acceleration I find the slope of the function describing your velocity and evaluate it at the given instant.
So:

`v'(t)=a(t)=2cos(2t)-9sin(9t)`

at `t=7/12pi`

`a(7/12pi)=2cos(2*7/12pi)-9sin(9*7/12pi)=4.6m/s^2`

So the impulse:

`"Impulse"=F*t=ma*t=3*4.6*7/12pi=25.3Ns`