Question

solving an equation for a given variable
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 ( a )?
( \frac{f - v}{t}=a )
( \frac{f + v}{t}=a )
( \frac{f}{t}-v=a )
( \frac{f}{t}+v=a )

Explanation:

Step1: Isolate the term with \(a\)

Given \(f = v+at\), subtract \(v\) from both sides:
\(f - v=at\)

Step2: Solve for \(a\)

Divide both sides by \(t\) (\(t
eq0\)):
\(\frac{f - v}{t}=a\)

Answer:

\(\frac{f - v}{t}=a\) (corresponding to the second - option if we assume the first option is \(\frac{f + v}{t}=a\), the second is \(\frac{f - v}{t}=a\), the third is \(\frac{f}{t}-v = a\) (incorrect algebra as \(f=v + at\) does not lead to this by standard manipulation), and the fourth is \(\frac{f}{t}+v=a\) (also incorrect))