Question

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

Answer 1

`"The Ins. Velo. at t=3 is "f'(3)=(6,e^3-6).`

Explanation:

The Instantaneous Velocity of an object moving in accordance to

`f(t)=(x(t),y(t))" at t=t_0, is, "f'(t_0)=(x'(t_0),y'(t_0)).`

Now, `f'(t)=(d/dt(t^2), d/dt(e^t-t^2))`.

`=(2t, e^t-2t)`

Therefore, inst. velo. at `t=3` is, `f'(3)=(6,e^3-6)`