Question

the equation $f = v + at$ represents the final velocity of an object, $f$, with an initial velocity, $v$, and an acceleration rate, $a$, over time, $t$.
which is an equivalent equation solved for $t$?
$t = \frac{f - a}{v}$
$t = v(f - a)$
$t = a(f - v)$
$t = \frac{f - v}{a}$

Explanation:

Step1: Start with the original equation

We have the equation \( f = v + at \). Our goal is to solve for \( t \). First, we need to isolate the term containing \( t \). To do this, we subtract \( v \) from both sides of the equation.
\( f - v = v + at - v \)
Simplifying the right - hand side, the \( v \) and \( -v \) cancel out, so we get \( f - v=at \).

Step2: Solve for t

Now that we have \( f - v = at \), we want to get \( t \) by itself. Since \( t \) is multiplied by \( a \), we divide both sides of the equation by \( a \) (assuming \( a
eq0 \)).
\( \frac{f - v}{a}=\frac{at}{a} \)
Simplifying the right - hand side, the \( a \) in the numerator and denominator cancels out, and we are left with \( t=\frac{f - v}{a} \).

Answer:

\( t=\frac{f - v}{a} \) (the last option among the given choices)