What is the instantaneous velocity of an object moving in accordance to # f(t)= (tlnt,e^(2t)) # at # t=2 #?

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Answer 1 · 2016-06-17T05:45:13

Instantaneous velocity of the object is #8.729#

Instantaneous velocity of an object moving in accordance to #f(t)=(tlnt,e^(2t))# at #t=2#, will be given by the value #(dy)/(dx)# at #t=2#.

As the object moves according to parametric form of equation given by #f(t)#,

#(dy)/(dx)=((dy)/(dt))/((dx)/(dt))#

= #(2e^(2t))/(txx1/t+1xxlnt)#

= #(2e^(2t))/(1+lnt)#

and at #t=2#,

#(dy)/(dx)=(2e^2)/(1+ln2)#

= #(2xx7.389)/(1+0.693)#

= #14.778/1.693#

= #8.729#

Hence, instantaneous velocity of the object is #8.729#