To find the correct equation for acceleration, let's go through each option step by step:
### Option 1: [tex]\( t = \frac{\Delta v}{a} \)[/tex]
1. Start with the formula:
[tex]\[ t = \frac{\Delta v}{a} \][/tex]
2. Rearrange this equation to solve for [tex]\( a \)[/tex] (acceleration):
[tex]\[ a = \frac{\Delta v}{t} \][/tex]
### Option 2: [tex]\( v_f = a t - v \)[/tex]
1. Start with the formula:
[tex]\[ v_f = a t - v \][/tex]
2. Rearrange this equation to solve for [tex]\( a \)[/tex] (acceleration):
[tex]\[ v_f + v = a t \][/tex]
[tex]\[ a = \frac{v_f + v}{t} \][/tex]
### Option 3: [tex]\( a = \frac{d}{t} \)[/tex]
1. The formula is already solved for [tex]\( a \)[/tex]:
[tex]\[ a = \frac{d}{t} \][/tex]
However, note that this formula relates distance ([tex]\( d \)[/tex]) and time ([tex]\( t \)[/tex]). Acceleration typically relates to the change in velocity over time, not purely distance over time.
### Option 4: [tex]\( \Delta v = \frac{a}{t} \)[/tex]
1. Start with the formula:
[tex]\[ \Delta v = \frac{a}{t} \][/tex]
2. Rearrange this equation to solve for [tex]\( a \)[/tex] (acceleration):
[tex]\[ a = \Delta v \times t \][/tex]
### Conclusion:
In classical mechanics, the correct and most commonly used equation for acceleration ([tex]\( a \)[/tex]) in terms of the change in velocity ([tex]\( \Delta v \)[/tex]) over time ([tex]\( t \)[/tex]) is:
[tex]\[ a = \frac{\Delta v}{t} \][/tex]
From the given options, the correct equation for acceleration is obtained by rearranging Option 1. Therefore, the correct option is:
[tex]\[ \boxed{1} \][/tex]
