The velocity of an object with a mass of 2 kg is given by v(t)= sin 5 t + cos 6 t . What is the impulse applied to the object at t= pi /4 ?

1 Answer
Feb 5, 2016

int F d t=-1,414212 " N.s"

Explanation:

J=int F.d t " 'impulse'"
M=int m.d v " 'momentum'"
int F. d t=int m. d v
v(t)=sin5t + cos6t
d v= (5 .cos5 t-6.sin6t)d t
int F.d t=m int (5. cos5t- 6. sin6t) d t
int F d t=2 (5 int cos5t d t- 6 int sin6t d t)
int F d t=2(5.1/5 .sin5t+ 6.1/6 cos 6t)
int F d t=2(sin 5t + cos 6t)
"for t="pi/4
int F d t=2(sin 5pi/4 + cos6pi/4)
int F d t=2(-0,707106+0)
int F d t=-1,414212 " N.s"