Question

multiple-choice question how do you find the distance a ball falls from rest in a given amount of time? $d = g cdot t$ $d = \frac{v_f - v_i}{-g}$ $d = \sqrt{\frac{2(v_f - v_i)}{g}}$ $d = \frac{1}{2}gt^2$

Explanation:

Step1: Recall free fall kinematics

For an object starting from rest ($v_i=0$), the kinematic equation for distance fallen under constant gravitational acceleration $g$ is derived from integrating acceleration over time.

Step2: Match to correct formula

The initial velocity $v_i=0$, so the simplified distance formula is $\frac{1}{2}gt^2$, which matches the last option.

Answer:

$d = \frac{1}{2}gt^2$