Question

multiple-choice question
how do you find the final velocity of an object in free-fall?
$v_f = v_i - g \cdot t$
$v_f = \frac{t - v_i}{-g}$
$v_f = \sqrt{\frac{2d}{g}}$
$v_f = \frac{1}{2}gt^2$

Explanation:

Step1: Recall free-fall kinematics

For free-fall, acceleration $a = g$ (downward, positive if we take direction of fall as positive). The first kinematic equation for velocity is $v_f = v_i + a t$. If we take upward as positive, $a=-g$, so $v_f = v_i - g t$.

Step2: Eliminate incorrect options

• Option 2: Rearranged wrong, not a valid kinematic formula.
• Option 3: Missing initial velocity; correct form without $v_i$ is $v_f=\sqrt{2gd}$, this has $\frac{2d}{g}$ inside root, wrong.
• Option 4: $\frac{1}{2}gt^2$ is displacement, not velocity.

Answer:

A. $v_f = v_i - g \cdot t$