Let the scenario be the following:
We have a driving car whose start velocity is $100\frac{m}{s}$ and it's brakes reduce the velocity by $10\frac{m}{s}$, quite simple.
If we were to make a vector function of distance-traveled vs velocity.
The velocity would be equal to:
$$y(t)=v - v_{brake}\cdot t$$
Because, for every time step, the brakes reduce the speed by the amount listed above eg $v_{brake}\cdot t$.
The distance traveled:
$$x(t)=y(t)\cdot t$$
My reasoning being:
$$distance = v\cdot t$$
A plot of the vector function:
Although this might seem pretty reasonable, it should be clear that the units don't add up. Velocity would be $\frac{m}{s} - m$, which is illegal according to the physics police. This would also invalidate the second function for distance traveled. I've probably overlooked something important.
Sorry for asking such a simple question.
The brakes reduce it's velocity by $10$ m/s in every second. So the acceleration is $-10 \, \text{m/s}^2$.
So $$y(t)=v-10\,\text{ms}^{-2}t$$
$$x(t)=100\,\text{ms}^{-1}t+\frac{1}{2}(-10\,\text{ms}^{-2})t^2$$