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The
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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. The mathematical definition of velocity (for one-dimensional motion) is:
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of Change [!copyright and waiver^SectionEdit.png!|Motion with Constant Velocity (Laws of Change)] Because of the extreme restrictions placed on the [systems|system] and [interactions|interaction] described by the [One-Dimensional Motion with Constant Velocity|1-D Motion (Constant Velocity)] [model], the [Law of Change] for the model is rather simple. The mathematical definition of [velocity] (for one-dimensional motion) is: {latex}\begin{large}\[ v \equiv \frac{dx}{dt}\]\end{large}{latex} If _v_ is a constant, this equation can be straightforwardly integrated: {latex} |
If v is a constant, this equation can be straightforwardly integrated:
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\begin{large}\[ \int_{t_{A}}^{t_{B}} v\:dt = \int_{x_{A}}^{x_{B}} dx \]\end{large}{latex}
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which
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(after
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algebraic
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rearrangement)
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gives:
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}\begin{large}\[ x_{B} = x_{A} + v(t_{B} - t_{A})\]\end{large}{latex} |
where:
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}\begin{large}\[ x_{A} \equiv x(t_{A}) \]\[x_{B} \equiv x(t_{B})\]\end{large}{latex} {note}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 {_}t{~}B{~}{_} - {_}t{~}A{~}{_}.{note} |
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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. |