To solve for [tex]\( t \)[/tex] in the given equation [tex]\( v = u + a t \)[/tex], we should follow these steps:
1. We start with the given equation:
[tex]\[
v = u + a t
\][/tex]
2. To isolate [tex]\( t \)[/tex], we need to get rid of the term [tex]\( u \)[/tex] on the right side. We do this by subtracting [tex]\( u \)[/tex] from both sides of the equation:
[tex]\[
v - u = a t
\][/tex]
3. Next, we want to solve for [tex]\( t \)[/tex]. To do so, we need to isolate [tex]\( t \)[/tex] by dividing both sides of the equation by [tex]\( a \)[/tex]:
[tex]\[
t = \frac{v - u}{a}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{C} \quad t = \frac{v - u}{a}
\][/tex]
