Is the Velocity of a Point Constant or Variable?

[Jack3145]

Homework Statement

A point: $$[x_{0}, y_{0}, z_{0}, t_{0}]$$
It's velocity: $$V_{a} = [v_{1}, v_{2}, v_{3}, v_{4}]$$

What is wrong with this equation:

$$x^{b} = [x_{0} + v_{1} * t, y_{0} + v_{2} * t, z_{0} + v_{3} * t, t_{0} + t]$$

 

[CompuChip]

Nothing is wrong with that, as long as V is a constant vector.
For example, if V_a = (2, 3, 4, 1) then your formula for x satisfies v = dx/dt.
However, if V_a = (3t, t², 3t - 12, t^2/6) it doesn't.