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#

The velocity of an object with a mass of 8 kg8 kg is given by v(t)= sin 5 t + cos 3 t v(t)= sin 5 t + cos 3 t . What is the impulse applied to the object at t= ( 3 pi)/ 4 t= ( 3 pi)/ 4 ?