Question

Rearrange the equation and find the value of $vf$in $d = \dfrac{1}{2}(vf + vi)t$?

Answer 1

Rearranging any equation means adjusting the equations such that similar terms come aside and then after taking common if possible the equation is simplified to its simplest possible form. For any such equation the first step is to simplify the brackets and make the equation very simple.

Complete step by step solution:
Firstly expand the equation then put all other elements on the equation on one side of equals to sign and the term for what we are searching for just make it alone on one side of equal to, then just simplify the equation by doing calculation and simplification. Here we used LCM rule in L.H.S of the equation, we had taken “t” common and then multiply by “vi” to simplify L.H.S part of equation, we get,

$$d = \dfrac{1}{2}(vf + vi)t \\\ \Rightarrow \dfrac{{2d}}{t} = vf + vi \\\ \Rightarrow \dfrac{{2d}}{t} - vi = vf \\\$$

The final answer should be in the best simplified form which is possible to obtain in equation, so on more simplification the best simple solution we can obtain for this equation is,
$\dfrac{{2d - vit}}{t} = vf$

Formulae Used: General expansion rule in algebra simple multiplication and cross multiplication.LCM is used (lowest common factor)

Note: This question can be solved only by expanding the equation. Expanding the equation means just do the simple math, i.e. plus, minus, division, multiplication and after doing that make the equation simple. You can follow and recheck your solution because cross multiplication and taking LCM sometimes, seems to be easy but can make you make certain calculation mistakes.