To solve for [tex]\( a \)[/tex] in the given formula [tex]\( V^2 = v^2 + 2 a s \)[/tex], let's manipulate the equation step by step:
1. Start with the original formula:
[tex]\[
V^2 = v^2 + 2 a s
\][/tex]
2. To isolate the term involving [tex]\( a \)[/tex], subtract [tex]\( v^2 \)[/tex] from both sides of the equation:
[tex]\[
V^2 - v^2 = 2 a s
\][/tex]
3. Now, to solve for [tex]\( a \)[/tex], we need to isolate [tex]\( a \)[/tex] by dividing both sides of the equation by [tex]\( 2 s \)[/tex]:
[tex]\[
a = \frac{V^2 - v^2}{2 s}
\][/tex]
Thus, the correct formula for [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{V^2 - v^2}{2 s}
\][/tex]
So, the correct choice among the given options is:
[tex]\[
\frac{v^2 - v^2}{2 s} = a
\][/tex]
Note that the correct formula is [tex]\( \frac{V^2 - v^2}{2 s} = a \)[/tex], based on the step-by-step manipulation of the original equation.
