Free Fall Formulas 499F3F

1. The problem asks for the formulas used in free fall motion. 2. Free fall refers to the motion of an object falling under the influence of gravity alone, with no air resistance. 3. The key formulas involve displacement $s$, initial velocity $v_0$, final velocity $v$, acceleration due to gravity $g$, and time $t$. 4. The acceleration due to gravity near Earth's surface is approximately $g = 9.8$ m/s$^2$ downward. 5. The main formulas are: - Velocity after time $t$: $$v = v_0 - g t$$ - Displacement after time $t$: $$s = v_0 t - \frac{1}{2} g t^2$$ - Velocity squared related to displacement: $$v^2 = v_0^2 - 2 g s$$ 6. Note the negative signs because gravity acts downward, so if upward is positive, gravity is negative. 7. These formulas assume upward direction is positive and acceleration due to gravity is constant. 8. They are derived from the equations of uniformly accelerated motion with acceleration $-g$. 9. For an object dropped from rest, $v_0 = 0$, so formulas simplify to: $$v = - g t$$ $$s = - \frac{1}{2} g t^2$$ 10. This means velocity increases downward linearly with time, and displacement increases quadratically. These are the fundamental formulas for free fall motion.