# The velocity of an object with a mass of #8 kg# is given by #v(t)= sin 5 t + cos 3 t #. What is the impulse applied to the object at #t= ( 3 pi)/ 4 #?

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Impulse at ( t = \frac{3\pi}{4} ): ( -m \cdot v'(t) )

Calculate the derivative of ( v(t) ) with respect to ( t ): ( v'(t) = 5 \cos(5t) - 3 \sin(3t) )

Evaluate ( v'(t) ) at ( t = \frac{3\pi}{4} ):

( v'\left(\frac{3\pi}{4}\right) = 5 \cos\left(\frac{15\pi}{4}\right) - 3 \sin\left(\frac{9\pi}{4}\right) )

Simplify the expression to find the impulse.

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