To solve for the acceleration \( a \) given the equation for the final velocity of an object in one-dimensional motion, we start with the formula:
[tex]\[ v = u + a t \][/tex]
where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.
Let's rearrange this equation to solve for \( a \).
1. Start with the given equation:
[tex]\[ v = u + a t \][/tex]
2. Subtract \( u \) from both sides to isolate the term involving \( a \):
[tex]\[ v - u = a t \][/tex]
3. To solve for \( a \), divide both sides of the equation by \( t \):
[tex]\[ a = \frac{v - u}{t} \][/tex]
Therefore, the correct expression for \( a \) is:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Now, let's examine the provided choices to find the correct one:
1. \( a = \frac{v + u}{t} \) – This is incorrect.
2. \( a = t(v + u) \) – This is incorrect.
3. \( a = t(v - u) \) – This is incorrect.
4. \( a = \frac{v - u}{t} \) – This is correct.
Hence, the correct choice is the fourth option:
[tex]\[ \boxed{4} \][/tex]
