Question

1. the distance a free - falling object has traveled can be modeled by the equation $d=\frac{1}{2}at^{2}$, where $a$ is acceleration due to gravity and $t$ is the amount of time the object has fallen. what is $t$ in terms of $a$ and $d$? 1) $t = sqrt{\frac{da}{2}}$ 2) $t=sqrt{\frac{2d}{a}}$ 3) $t = (\frac{da}{d})^{2}$ 4) $t = (\frac{2d}{a})^{2}$

Explanation:

Step1: Isolate $t^{2}$

Given $d=\frac{1}{2}at^{2}$, multiply both sides by 2 to get $2d = at^{2}$. Then divide both sides by $a$: $t^{2}=\frac{2d}{a}$.

Step2: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and is non - negative in this context, $t=\sqrt{\frac{2d}{a}}$.

Answer:

1. $t = \sqrt{\frac{2d}{a}}$