Because the initial position and initial time can be arbitrarily chosen, it is possible to rewrite all these equations in terms of only 5 variables by defining:\\
{center}{latex}\begin{large}\[ \Delta x \equiv x_{f}-x_{i} \]\[\Delta t \equiv t_{f}-t_{i}\]\end{large}{latex}{center}\\
If you replace the initial and final positions and times with these "deltas", then each of the equations given above involves exactly four unknowns. Interestingly, the four equations represent all but _one_ of the unique combinations of four variables chosen from five possible unknowns. Which unique combination is missing? Can you derive the appropriate "fifth equation"? |