Free Fall: Vertical Motion Under Gravity

A set of vocabulary flashcards covering the fundamental concepts, kinematic equations, formulas for upward motion, and common misconceptions regarding Free Fall and Vertical Motion Under Gravity.

Free Fall

Any motion where gravity alone acts on an object, producing a constant downward acceleration of $9.81\,m/s^2$, regardless of whether the object is moving upward or downward.

Acceleration due to gravity ($g$)

A constant value of $9.81\,m/s^2$, always directed downward, that applies to all objects in ideal conditions without air resistance regardless of mass or shape.

Sign Convention (Session Convention)

The system where Upward is defined as Positive (+$) and Downward is Negative (-$), meaning acceleration due to gravity is written as$a = -9.81\,m/s^2$$.

Dropped Object

An object that begins its motion from rest, characterized by an initial velocity of $v_i = 0$.

Velocity-time Equation

A kinematic equation expressed as $v_f = v_i + at$ used to determine an object's final velocity.

Displacement-time Equation

A kinematic equation expressed as $d = v_i \cdot t + \frac{1}{2}at^2$ used to determine vertical displacement over time.

Velocity-displacement Equation

A kinematic equation expressed as $v_f^2 = v_i^2 + 2ad$ which relates speed and distance.

Simplified speed after time ($t$)

A simplified formula for dropped objects where $v_f = g \cdot t$, with $g$ taken as $9.81\,m/s^2$.

Simplified distance fallen in time ($t$)

A simplified formula for dropped objects where $d = \frac{1}{2} \cdot g \cdot t^2$.

Simplified speed after distance ($d$)

A simplified formula for objects starting from rest where $v_f^2 = 2 \cdot g \cdot d$.

GUESS Framework

A step-by-step problem-solving method consisting of five parts: G (Given), U (Unknown), E (Equation), S (Substitution), and S (Solution).

The Peak

The point in an upward-thrown object's flight where it is momentarily at rest, resulting in a final velocity of $v_f = 0\,m/s$.

Maximum Height ($h$) formula

A derived formula for upward-thrown objects calculated as $h = \frac{v_i^2}{2g}$, using $g = 9.81\,m/s^2$.

Time to Peak ($t_{peak}$) formula

A derived formula for the time required to reach maximum height, calculated as $t_{peak} = \frac{v_i}{g}$.

Total Flight Time ($t_{total}$)

The full duration of an up-and-down journey, calculated as $t_{total} = 2 \times t_{peak}$ due to the symmetry of free fall.

Symmetry of Free Fall

The concept that the trip up is a mirror image of the trip down in terms of time, speed, and distance; for example, speed at any height going up equals speed at the same height coming down.

Galileo's Principle of Free Fall

The physical law stating that all objects fall at the same rate of $g = 9.8\,m/s^2$ regardless of their mass.

Peak Acceleration Misconception

The incorrect belief that acceleration is zero at the peak of flight; in reality, acceleration is ALWAYS $-9.81\,m/s^2$ throughout the entire motion.