What is the instantaneous velocity of an object moving in accordance to # f(t)= (2sin(2t+pi),t-sec(t/2)) # at # t=pi/3 #?

1 Answer
Bhaskar B.
Mar 3, 2018

#vecV = 2hati+2/3hatj#

Explanation:

The object is performing 2 dimensional motion. Its position vector can be resolved into the following:
#vec R = ( 2sin(2t + pi)hat i+ t-sec(t/2) hatj)#
where #hati , hatj# are unit vectors in the x and y direction.

Now, the velocity is the first derivative of its position with respect to time. Therefore,

#d/dtvec R = vec V# where #vec V# is the velocity vector.

#d/dtvecR = d/dt( 2sin(2t + pi)hat i+ t-sec(t/2) hatj)#
#=> vec V = (-4cos(2t))hati + (1 - 2 sin^3(t/2) csc^2(t))hatj#

plugging in #t = pi/3#

#vec V = 2hati+2/3hatj#

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