What is the instantaneous velocity of an object moving in accordance to # f(t)= (sin^2t,cos3t) # at # t=pi/12 #?

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Answer 1 · 2017-11-26T16:04:51

The instantaneous velocity is #=(0.5, -2.12)#

#(sint)'=cost#

#(cost)'=-sint#

The velocity is the derivative of the position

#f(t)=(sin^2t,cos3t)#

#v(t)=f'(t)=(2sintcost, -3sin3t)#

Therefore, when #t=1/12pi#

#v(1/12pi)=(2sin(1/12pi)cos(1/12pi), -3sin(3/12pi))#

#=(0.5, -2.12)#