Students who successfully complete this primer will be able to:

Understand that expert physics problem$-$solvers associate quantities with variables and solve for unknowns in terms of these variables.

Simplify algebraic relationships for expressions that are commonly encountered in physics.

For additional practice, you may want to review$$Rearrangement of Algebraic Expressions.

It is widely believed that it is easier to work physics problems by substituting numerical values in at the very beginning of the problem. However, expert physics problem$-$solvers will typically solve physics problems using variables, and substitute known values only as a final step, because this approach is generally faster, easier, reduces mistakes, and results in a better and more general understanding of physics. This approach may take a little practice and effort initially, but it has important benefits. Throughout this primer are several techniques that are useful for simplifying physical relationships expressed in terms of variables.

Technique $1$ :$$Substitute in known values of $0$ that will simplify expressions $($this is the exception to the rule that known numerical values should only be substituted in at the final step$).$

Example: Analysis of the physics of a system indicates that an appropriate expression describing it is given by:$$x$=$x$0+$v$0$t$+12$at$2$x$=$x$0+$v$0$t$+12$at$2.$The problem requires solving for$$aa$,$ and the known values for the system are$$x$=3\mathrm{.}50$meterx$=3\mathrm{.}50$meter,$$x$0=1\mathrm{.}50$meterx$0=1\mathrm{.}50$meter,$$v$0=0$meter$/$secondv$0=0$meter$/$second$,$ and$$t$=0\mathrm{.}639$secondt$=0\mathrm{.}639$second.$$In this case, substituting in the known value of $0$ would be the next step in the analysis, resulting in: x$=$x$0+12$at$2$x$=$x$0+12$at$2.$

Part A

Imagine you derive the following expression by analyzing the physics of a particular system:$$v$2=$v$20+2$axv$2=$v$02+2$ax$.$ The problem requires solving for$$xx$,$ and the known values for the system are a$=2\mathrm{.}55$meter$/$second$2$a$=2\mathrm{.}55$meter$/$second$2,$v$0=21\mathrm{.}8$meter$/$secondv$0=21\mathrm{.}8$meter$/$second$,$ and$$v$=0$meter$/$secondv$=0$meter$/$second$.$ Perform the next step in the analysis.$$

View Available Hint$($s$)$for Part A

$$v$2=$v$20+2$axv$2=$v$02+2$ax$($no simplification should be performed on the expression in this situation$)0=$v$20+2$ax$0=$v$02+2$ax$$v$2=(21\mathrm{.}8$meter$/$second$)2+2(2\mathrm{.}55$meter$/$second$2)$xv$2=(21\mathrm{.}8$meter$/$second$)2+2(2\mathrm{.}55$meter$/$second$2)$x$$