The Law of Change null
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. The mathematical definition of velocity (for one-dimensional motion) is:
\begin
[ v \equiv \frac
]\end
If v is a constant, this equation can be straightforwardly integrated:
\begin
[ \int_{t_{A}}{t_{B}} v\:dt = \int_{x_{A}}{x_{B}} dx ]\end
which (after algebraic rearrangement) gives:
\begin
[ x_
= x_
+ v(t_
- t_
)]\end
where:
\begin
[ x_
\equiv x(t_
) ][x_
\equiv x(t_
)]\end
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". Elapsed time is equivalent to the difference tB - tA.