What is the instantaneous velocity of an object moving in accordance to # f(t)= (t/(t-5),3t-2) # at # t=-2 #?

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Answer 1 · 2017-04-16T00:34:46

About #3.002# at an angle of #-1.536#

Take the derivative of #f(t)#. Don't' forget quotient rule:

#f'(t)=(((1)(t-5)-(t)(1))/(t-5)^2,3)#

Simplify:

#f'(t)=((t-5-t)/(t-5)^2,3)#

#f'(t)=(-5/(t-5)^2,3)#

Now plug in #t=--2#

#f'(-2)=(-5/(-2-5)^2,3)#

#f'(-2)=(-5/49,3)#

Now we have the velocity in the #x# direction and #y# direction. Use Pythagorean theorem.

#(-5/49)^2+(3)^2=c^2#

Solve for #c#:

#c~~3.002#

We can find the angle of this velocity with tangents:

#tan(theta)=3/(-5/49)#

#theta=-1.536#