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 #?

1 Answer
Dec 19, 2015

Answer:

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#