To solve the given equation [tex]\( f = v + at \)[/tex] for [tex]\( t \)[/tex], follow these steps:
1. Understand the original equation:
The equation [tex]\( f = v + at \)[/tex] represents the final velocity ([tex]\( f \)[/tex]) of an object with an initial velocity ([tex]\( v \)[/tex]) and an acceleration rate ([tex]\( a \)[/tex]) over a time period ([tex]\( t \)[/tex]).
2. Isolate the term involving [tex]\( t \)[/tex]:
We need to solve for [tex]\( t \)[/tex], so let's isolate the term [tex]\( at \)[/tex] on one side of the equation.
Start with the original equation:
[tex]\[
f = v + at
\][/tex]
3. Subtract [tex]\( v \)[/tex] from both sides:
To isolate [tex]\( at \)[/tex], subtract [tex]\( v \)[/tex] from both sides of the equation:
[tex]\[
f - v = at
\][/tex]
4. Solve for [tex]\( t \)[/tex]:
Now, to isolate [tex]\( t \)[/tex], divide both sides of the equation by [tex]\( a \)[/tex]:
[tex]\[
t = \frac{f - v}{a}
\][/tex]
So, the equivalent equation solved for [tex]\( t \)[/tex] is:
[tex]\[
t = \frac{f - v}{a}
\][/tex]
Therefore, the correct answer is:
[tex]\[
t = \frac{f - v}{a}
\][/tex]
