To solve the equation [tex]\( v - u = a \cdot t \)[/tex] for [tex]\( t \)[/tex], follow these steps:
1. Understand the given equation:
[tex]\[
v - u = a \cdot t
\][/tex]
This is a linear equation where [tex]\( v \)[/tex] and [tex]\( u \)[/tex] are constants, and we want to solve for [tex]\( t \)[/tex].
2. Isolate [tex]\( t \)[/tex]:
To solve for [tex]\( t \)[/tex], we need to get [tex]\( t \)[/tex] by itself on one side of the equation. Since [tex]\( t \)[/tex] is being multiplied by [tex]\( a \)[/tex], we can isolate [tex]\( t \)[/tex] by dividing both sides of the equation by [tex]\( a \)[/tex].
3. Divide both sides by [tex]\( a \)[/tex]:
[tex]\[
\frac{v - u}{a} = \frac{a \cdot t}{a}
\][/tex]
The [tex]\( a \)[/tex] on the right-hand side cancels out, leaving:
[tex]\[
\frac{v - u}{a} = t
\][/tex]
4. Write the final solution:
[tex]\[
t = \frac{v - u}{a}
\][/tex]
Therefore, the correct answer is:
[tex]\[
t = \frac{v - u}{a}
\][/tex]
This shows the step-by-step process to isolate [tex]\( t \)[/tex] and solve the equation.
