Can someone teach how to solve formula manipulation/transformation in Physics??
You solve these the same way you would solve them if the A, t, and v are just numbers (which in reality they are.)
Step by step:
$\displaystyle A = at + v$
$\displaystyle A - v = at + v - v$
$\displaystyle A - v = at$
$\displaystyle \frac{A - v}{t} = \frac{at}{t}$
$\displaystyle a = \frac{A - v}{t}$
For $\displaystyle V_0$:
$\displaystyle S = V_0t + \frac{1}{2}at^2$
$\displaystyle S - \frac{1}{2}at^2 = V_0t + \frac{1}{2}at^2 - \frac{1}{2}at^2$
$\displaystyle V_0t = S - \frac{1}{2}at^2$
$\displaystyle \frac{V_0t}{t} = \frac{S - \frac{1}{2}at^2}{t}$
$\displaystyle V_0 = \frac{S}{t} - \frac{1}{2}at$
You solve for a.
-Dan