Question 147965
Solve: {{{v^2 = V[0]^2+2as}}} for {{{V[0]}}}, {{{s}}}, and {{{a}}}
To solve a formula for a particular variable means that you must rearrange (manipulate) the formula so that the variable in question is on one side of the = sign, and everything else is on the other side, by using the standard rules of algebra.
1) Solve for {{{V[0]}}}:
{{{v^2 = V[0]^2+as}}} subtract as from both sides.
{{{v^2-as = V[0]^2}}} Now take the square root of both sides.
{{{sqrt(v^2-as) = V[0]}}} or {{{V[0] = sqrt(v^2-as)}}}
2) Solve for s:
{{{v^2 = V[0]^2+as}}} Subtract {{{V[0]^2}}} from both sides.
{{{v^2-V[0]^2 = as}}} Now divide both sides by a.
{{{((v^2-V[0]^2))/a = s}}} or {{{s = ((v^2-V[0]^2))/a}}}
3) Solve for a:
{{{v^2 = V[0]^2+as}}} Subtract {{{V[0]^2}}} from both sides.
{{{v^2-V[0]^2 = as}}} Now divide both sides by s.
{{{((v^2-V[0]^2))/s = a}}} or {{{a = ((v^2-V[0]^2))/s}}}