Question

What is the instantaneous velocity of an object moving in accordance to `f(t)=(12-t,t^2-t+7)` at `t=1`?

Answer 1

`vec(v(1)) = (v_x(t), v_y(t)) = (11, 7)`
The question is incorrect it is written in scalar form. What you are looking is the components of the velocity (a vector). See explanation... Make sure you discuss this with your teacher and ensure you both understand the difference between a vector (velocity) and a scalar (speed).

Explanation:

A couple of things on this question. You're implying a vector quantity in 2D, yet you wrote the equation as if it was a scalar. This maybe how your teacher set the problem, but it is not correct. The way it should be set is as follows:
`vec(v(t)) = (v_x(t), v_y(t)) = (12-t, t^2 - t +7)`
Note here you can see that the velocity has motion in both the horizontal and vertical direction given by:
`v_x = 12 - t; v_y = t^2 - t + 7`
Now evaluate the value of each components of velocity at t = 1
`v_x = 11; v_y =7`
`vec(v(1)) = (v_x(t), v_y(t)) = (11, 7)`