Given the formula for the final velocity of an object:
[tex]\[ v = u + at \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity,
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( t \)[/tex] is the time.
We need to solve this equation for the acceleration [tex]\( a \)[/tex].
1. Start with the original equation:
[tex]\[ v = u + at \][/tex]
2. To isolate [tex]\( a \)[/tex], first subtract [tex]\( u \)[/tex] from both sides of the equation:
[tex]\[ v - u = at \][/tex]
3. Now, to solve for [tex]\( a \)[/tex], divide both sides of the equation by [tex]\( t \)[/tex]:
[tex]\[ \frac{v - u}{t} = a \][/tex]
Therefore, the solution for [tex]\( a \)[/tex] is:
[tex]\[ a = \frac{v - u}{t} \][/tex]
So, the correct choice from the given options is:
[tex]\[ a = \frac{v - u}{t} \][/tex]
