Question

which equation can be used to solve for acceleration?
\\( t = \frac{\delta v}{a} \\)
\\( v_f = at - v_i \\)
\\( a = \frac{\delta v}{t} \\)
\\( \delta v = \frac{a}{t} \\)

Explanation:

Step1: Recall the formula for acceleration

The formula for acceleration \(a\) is \(a=\frac{\Delta v}{t}\), where \(\Delta v\) is the change in velocity and \(t\) is the time.

Step2: Rearrange the formula to solve for \(a\)

Starting from \(a = \frac{\Delta v}{t}\), we can multiply both sides by \(t\) to get \(\Delta v=at\). Rearranging for \(a\) gives \(a=\frac{\Delta v}{t}\).

Answer:

\(a=\frac{\Delta v}{t}\) (the first option \(\Delta v = at\) can be rearranged to \(a=\frac{\Delta v}{t}\) which is the formula for acceleration. The second option \(a=\frac{t}{a}\) is incorrect algebraically. The third option \(v_f=at - v_i\) is the formula \(v_f=v_i + at\) rearranged incorrectly. The fourth option \(t=\frac{a}{\Delta v}\) is also incorrect as it does not represent the formula for acceleration)