Question

What is the instantaneous velocity of an object with position at time t equal to `f(t)= ((t-2)^2,5t-3)` at `t=2`?

Answer 1

Instantaneous velocity is `5`.

Explanation:

In a parametric form regarding position of an object `f(t)=(x(t),y(t))`,

we get two component of velocity `(dx)/(dt)` and `(dy)/(dt)`, which are at right angles to each other

Here we have `f(t)=((t-2)^2,5t-3)`

hence two components are `2(t-2)` and `5` and at `t=2`

these are `0` and `5`

and hence instantaneous velocity is `sqrt(0^2+5^2)=sqrt25=5`.