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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Answer 1 · 2016-01-13T17:30:14

#11.3137 kg.m//s#

Impulse may be given as change in momentum as follows by #I(t)=Fdt=mdv#.

#therefore I(t)=mdv#

#=md/dt(sin5t+cos3t)#

#=8(5cos5t-3sin3t)#

#=40cos5t-24sin3t#

#thereforeI((3pi)/4)=40cos((5*3pi)/4)-24sin((3*3pi)/4)#

#=40/sqrt2-24/sqrt2#

#=16/sqrt2#

#11.3137 kg.m//s#