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

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Answer 1 · 2016-01-02T04:37:08

#0.172261#

The instantaneous velocity is equal to #f'(pi/3)#.

#x(t)=t^2sin(t-pi)#

To find #x'(t)#, use the product rule.

#x'(t)=2tsin(t-pi)+t^2cos(t-pi)#

We also know that

#y(t)=tcost#

Again, differentiate with the product rule.

#y'(t)=cost-tsint#

The derivative of the entire parametric equation is found as follows:

#f'(t)=(y'(t))/(x'(t))=(cost-tsint)/(2tsin(t-pi)+t^2cos(t-pi))#

Find #f'(pi/3)#.

#f'(pi/3)=(cos(pi/3)-pi/3sin(pi/3))/(2(pi/3)sin(pi/3-pi)+(pi/3)^2cos(pi/3-pi))#

#approx0.172261#