The velocity of an object with a mass of #8 kg# is given by #v(t)= sin 4 t+ cos 13 t #. What is the impulse applied to the object at #t= ( 3 pi)/ 4 #?

Answer 1

#bar J=5,656 " N.s"#

#bar J=int F(t)*d t# #F=m*a=m*(d v)/(d t)# #bar J=int m*(d v)/(d t)*d t# #bar J=m int d v# #d v=(4cos4t -13sin13t)*d t# #bar J=m int (4cos4t-13sin13t)*d t# #bar J=m(sin4t+cos13t)# #bar J=8(sin4*3pi/4+cos13*3pi/4)# #bar J=8*(0+0,707)# #bar J=8*0,707# #bar J=5,656 " N.s"#

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Answer 2

Nicholas Agrusa

To find the impulse applied to the object at ( t = \frac{3\pi}{4} ), you first need to find the velocity at that time, and then calculate the change in momentum, which is the impulse. Given the velocity function ( v(t) = \sin(4t) + \cos(13t) ), plug in ( t = \frac{3\pi}{4} ) to find the velocity at that time. Then, multiply the velocity by the mass of the object to get the impulse.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.