Question

which equation can be used to solve for acceleration?
① (t=\frac{delta v}{a})
② (v_f = at - v_i)
③ (a=\frac{d}{t})
④ (delta v=\frac{a}{t})

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{t}$, where $\Delta v$ is the change in velocity and $t$ is the time - interval. We can re - arrange this formula.

Step2: Analyze each option

• Option 1: $t=\frac{\Delta v}{a}$ can be re - arranged from $a = \frac{\Delta v}{t}$, which is correct for finding acceleration when we know $\Delta v$ and $t$.
• Option 2: $v_f=at + v_i$ (the correct kinematic equation is $v_f=v_i+at$), and $v_f = at - v_i$ is incorrect.
• Option 3: $a=\frac{d}{t}$ is incorrect. The formula $a=\frac{d}{t}$ is not the acceleration formula. The correct relationship for motion with constant acceleration involves velocity changes over time.
• Option 4: $\Delta v=\frac{a}{t}$ is incorrect. The correct formula is $\Delta v = at$.

Answer:

$t=\frac{\Delta v}{a}$ (first option)