To solve the equation for [tex]\( t \)[/tex] in the formula [tex]\( v = u + a t \)[/tex], we need to isolate [tex]\( t \)[/tex]. Here is a step-by-step solution:
1. Start with the given equation:
[tex]\[
v = u + a t
\][/tex]
2. Subtract [tex]\( u \)[/tex] from both sides to begin isolating [tex]\( t \)[/tex]:
[tex]\[
v - u = a t
\][/tex]
3. Divide both sides by [tex]\( a \)[/tex] to solve for [tex]\( t \)[/tex]:
[tex]\[
t = \frac{v - u}{a}
\][/tex]
Thus, the time [tex]\( t \)[/tex] can be expressed in terms of the initial velocity [tex]\( u \)[/tex], the final velocity [tex]\( v \)[/tex], and the acceleration [tex]\( a \)[/tex] as:
[tex]\[
t = \frac{v - u}{a}
\][/tex]
