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

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

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

Answer

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{t}$, where $\Delta v$ is change - in velocity and $t$ is time. We can re - arrange the formula $t = \frac{\Delta v}{a}$ to solve for acceleration as $a=\frac{\Delta v}{t}$.

Step2: Analyze each option

  • Option 1: $t=\frac{\Delta v}{a}$ can be re - arranged to $a = \frac{\Delta v}{t}$, which is the correct formula for acceleration.
  • Option 2: The correct equation of motion is $v_f=v_i + at$, not $v_f=at - v_i$.
  • Option 3: $a=\frac{d}{t}$ is incorrect. The correct relationship involving distance $d$, time $t$ and acceleration $a$ for uniformly accelerated motion starting from rest is $d=\frac{1}{2}at^{2}$.
  • Option 4: $\Delta v=\frac{a}{t}$ is incorrect. The correct formula is $\Delta v = at$.

Answer:

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