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

##### 1 Answer

Jan 2, 2016

#### Explanation:

The instantaneous velocity is equal to

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

To find

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

#approx0.172261#