Free Fall Motion Formulas

This page focuses on the caduta dei gravi (free fall of objects), which is a special case of uniformly accelerated motion where the acceleration is due to gravity.

Definition: Free fall is the motion of an object under the influence of gravity alone, neglecting air resistance.

The page presents key formulas for free fall motion:

• Velocity formula: v = gt
• Displacement formula: s = ½gt²

Where 'g' is the acceleration due to gravity (approximately 9.8 m/s² on Earth's surface).

Highlight: In free fall, all objects accelerate at the same rate regardless of their mass, a principle first demonstrated by Galileo Galilei.

The page also includes formulas for calculating the time and height of maximum altitude for objects thrown upward:

• Time to reach maximum height: t_max = v₀ / g
• Maximum height reached: s_max = v₀² / (2g)

Where v₀ is the initial upward velocity.

Example: If you throw a ball straight up with an initial velocity of 20 m/s, you can calculate the maximum height it will reach using s_max = v₀² / (2g) = 20² / (2 * 9.8) ≈ 20.4 meters.

Vocabulary: "Caduta dei gravi" is Italian for "fall of heavy bodies" or simply "free fall" in physics contexts.

These formulas are essential for solving problems related to moto di caduta dei gravi (motion of falling objects) and understanding the behavior of objects in free fall.

Uniformly Accelerated Motion (MRUA) Formulas

This page presents essential formulas for moto rettilineo uniformemente accelerato (uniformly accelerated rectilinear motion). These equations are fundamental for understanding and solving problems related to motion with constant acceleration.

Definition: MRUA (Moto Rettilineo Uniformemente Accelerato) refers to motion in a straight line with constant acceleration.

The page displays various formulas for MRUA, including:

• Displacement formula: s = ½at² + v₀t + s₀
• Velocity formula: v = at + v₀
• Acceleration formula: a = (v - v₀) / t

Highlight: The formulas presented allow for the calculation of any variable (displacement, velocity, acceleration, or time) when given the others.

Inverse formulas are also provided, which are useful for solving problems when certain variables are unknown. For example:

• Time can be calculated using t = (v - v₀) / a
• Initial velocity can be found with v₀ = v - at

Example: To find the displacement of an object undergoing uniformly accelerated motion, you would use the formula s = ½at² + v₀t + s₀, where 'a' is acceleration, 't' is time, v₀ is initial velocity, and s₀ is initial position.

The page also includes a special formula for calculating displacement using initial and final velocities: s = (v² - v₀²) / (2a)

Vocabulary: MRUA stands for "Moto Rettilineo Uniformemente Accelerato" in Italian, which translates to "Uniformly Accelerated Rectilinear Motion" in English.