Answered

The equation [tex]$f = v + at$[/tex] represents the final velocity of an object, [tex]$f$[/tex], with an initial velocity, [tex][tex]$v$[/tex][/tex], and an acceleration rate, [tex]$a$[/tex], over time, [tex]$t$[/tex].

Which is an equivalent equation solved for [tex][tex]$t$[/tex][/tex]?

A. [tex]$t = \frac{f - v}{a}$[/tex]
B. [tex]$t = \frac{f - a}{v}$[/tex]
C. [tex][tex]$t = a(t - v)$[/tex][/tex]
D. [tex]$t = v(f - a)$[/tex]



Answer :

GinnyAnswer
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]