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 time. Rearranging this formula gives $t = \frac{\Delta v}{a}$.

Step2: Analyze each option

• Option 1: $t=\frac{\Delta v}{a}$ can be rearranged to solve for $a$ as $a = \frac{\Delta v}{t}$, so this is correct for finding acceleration.
• Option 2: $v_f=at - v_i$ is incorrect. The correct kinematic - equation is $v_f=v_i + at$.
• Option 3: $a=\frac{d}{t}$ is incorrect. This is the formula for average speed ($v=\frac{d}{t}$), not acceleration.
• Option 4: $\Delta v=\frac{a}{t}$ is incorrect. The correct relationship is $\Delta v = at$.

Answer:

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