Question

What is the instantaneous velocity of an object moving in accordance to `f(t)= (ln(t^2),3t-2)` at `t=2`?

Answer 1

Instantaneous velocity at `t=2` is `1/3`

Explanation:

When an object moves in accordance to `f(t)=(ln(t^2),3t-2)`

its instantaneous velocity is given by `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

As in parametric equation `y=ln(t^2)` and `x=3t-2`

`(dy)/(dt)=2txx1/t^2=2/t` and `(dx)/(dt)=3` or

`(dy)/(dx)=(2/t)/3=2/(3t)`

Hence, instantaneous velocity at `t=2` is `2/(3xx2)=1/3`