Video summary

Fórmulas de Caída Libre @MatematicasprofeAlex

Main summary

Key takeaways

Educational

Main ideas / concepts

  • Goal of the video: Explain the free-fall formulas and—more importantly—why different physics teachers/textbooks use different sign conventions (positive/negative) for the same physical situation, while still producing the same correct results when used consistently.

Connection to uniformly accelerated motion

  • Free fall is treated as uniformly accelerated motion.
  • In classic uniformly accelerated motion examples, distance is along a horizontal axis (x).
  • In free fall, motion is vertical, so the same kinematics applies but with:
    • x replaced by y (vertical displacement/height)
    • acceleration “a” replaced by gravitational acceleration “g”

Formulas: what to use and what not to use

  • While the uniformly accelerated motion set often contains five related equations, the instructor says that for free fall you only need three key formulas to solve exercises.
  • Certain formulas are avoided primarily because they either:
    • isolate gravity (but in most textbook problems you already know the value of g, typically Earth’s 9.8 m/s²), or
    • are considered less directly useful (because gravity is already known and the formula doesn’t match the typical structure used in exercises).

Methodology: sign conventions + formulas

A) Coordinate/variable changes for free fall

  • Replace:
    • Distance variable: (x \rightarrow y)
    • Acceleration: (a \rightarrow g)
  • Interpret the motion as vertical:
    • Downward motion corresponds to one direction (the y-axis direction is vertical)
    • Upward motion corresponds to the opposite direction

B) The three free-fall formulas to use in this course

The instructor states that, in this course, you will use these three formulas for free fall (uniformly accelerated motion with gravity):

  1. Final velocity [ v_f = v_i + g\,t ]

  2. Height/displacement [ y = v_i\,t + \dfrac{g\,t^2}{2} ]

  3. Final velocity squared [ v_f^2 = v_i^2 + 2g\,y ]

Notes from the video:

  • If some textbooks write “more or less” in a formula, the instructor says their course will use the consistent sign convention and treat the terms normally—emphasizing consistent positive values according to their convention.
  • The instructor also mentions that in some texts:
    • height might be written as H instead of y, but it refers to the same physical idea.

C) How to handle positive/negative values (most important lesson)

Core instruction: Signs don’t matter by themselves—consistency does. Different teachers pick different conventions, but results match if applied correctly.

1) Identify which quantities are scalars vs vectors

  • Scalar quantities (no direction/sign):

    • Time is treated as scalar → always positive.

  • Vector quantities (direction/sign matters):

    • Displacement/height ( (y) or (H) )
    • Gravity (acceleration due to gravity)
    • Initial velocity
    • Final velocity

2) Two possible direction conventions—choose one and be consistent

Option used in this course for downward motion (falling):

  • Decide that downward vectors are positive.
  • Therefore, in a falling-only situation (downward motion):
    • height/displacement: positive (downward)
    • gravity: positive (points downward)
    • initial velocity: positive (downward direction)
    • final velocity: positive (downward direction)

Because gravity and the motion are in the same direction here, signs become straightforward, and the instructor says we don’t need sign symbols in the formulas for that case.

Convention for upward launch (throwing upward):

  • When the object goes up, most values are positive for the upward direction, but:
  • Gravity is always directed downward, so under the “upward positive” convention:
    • gravity must be negative

Instructor’s rule of thumb for upward problems:

  • If upward motion is positive, then gravity is the only negative vector (because it points opposite to the chosen positive direction).

3) What to do if you choose the opposite convention

  • Some textbooks take:
    • downward = negative and upward = positive.
  • That is valid, but you must interpret signs correctly.
    • Example (conceptual): if upward is positive and you calculate a velocity as negative, it means the velocity is actually in the downward direction.

Speakers / sources featured

  • Speaker: “MatematicasprofeAlex” — the instructor/creator of the video (referred to as “Teacher/Alex” in the subtitles).

Original video