The Law of Change
Because of the extreme restrictions placed on the systems and interactions described by the One-Dimensional Motion with Constant Velocity model, the Law of Change for the model is rather simple. If velocity is constant, it can be found mathematically by the expression:
\begin
[ v \equiv \frac
= \frac{x_
- x_{i}}{t_
-t_{i}}]\end
Note that the first equality is the definition of velocity, which always holds. The second equality is only true if the velocity is constant.
where:
\begin
[ x_
\equiv x(t_
) ][x_
\equiv x(t_
)]\end
It is important to note that the Law of Change for this model is usually even simpler than the form written above! It is rare for physics problems to specify an initial time for a motion, but rather they will usually specify an elapsed time. For instance, instead of saying "a car began a trip at 10:05 AM and drove until 10:15 AM", the problem will usually specify only that the car drove "for 10 minutes". Thus, it is usual to choose the origin of the time coordinate such that ti = 0, which simplifies the equation.