Per Second per Second

• Per-Second-per-Second-I.mp3
• Per-Second-per-Second-I.mp4
• Per-Second-per-Second-II.mp3
• Per-Second-per-Second-II.mp4
• Per-Second-per-Second-intro.mp3

[Intro]
Thirty-two feet
(Per second per second)
Oh, that’s deep
(Square aware)

[Verse 1]
Which falls faster
An egg or a rock
Why at the same clock
Though the egg’s a disaster

[Chorus]
Thirty-two feet
(Per second per second)
Oh, that’s deep
(Square aware)

[Bridge]
Falling (falling fast)
Falling faster (as time goes past)
32, 64, 128
(An exponential rate)

[Verse 2]
Now I’ve come to know
How fast things go
There for a second…
I had to reckon

[Chorus]
Thirty-two feet
(Per second per second)
Oh, that’s deep
(Square aware)

[Bridge]
Falling (falling fast)
Falling faster (as time goes past)
32, 64, 128
(An exponential rate)

[Chorus]
Thirty-two feet
(Per second per second)
Oh, that’s deep
(Square aware)

[Outro]
I’m aware
(Squared there)

A SCIENCE NOTE

What Does “Per Second Per Second” Mean?

• “Per second per second” refers to acceleration, the rate at which velocity changes over time. For example:
  • If an object’s velocity increases by 10 m/s1 every second, it has an acceleration of 10 m/s2.
  • This is read as “meters per second squared” or “meters per second per second.”

How Fast Does an Object Fall?

• Near the surface of the Earth, objects fall with an acceleration due to gravity, denoted by $g$, approximately 9.8 m/s2 (or 32 ft/s2 — 32 feet per second per second).
• Assuming no air resistance, the speed of a falling object can be calculated using the formula:v=g⋅t
  where:
  • v is the velocity,
  • g=9.8 m/s2
  • t is the time in seconds.

  Example:

  • After 1 second: v=9.8 m/s     v = 9.8.
  • After 2 seconds: v=19.6 m/s  v = 19.6.
  • After 3 seconds: v=29.4 m/s  v = 29.4

Do Objects Fall at the Same Speed Regardless of Weight?

• In the absence of air resistance (in a vacuum), all objects fall at the same rate regardless of their mass. This is because the force of gravity acts equally on all objects relative to their mass.
  • Example: A feather and a hammer will fall at the same rate in a vacuum (as demonstrated during the Apollo 15 moon landing).
• With air resistance, heavier or denser objects usually fall faster because they are less affected by drag. For example:
  • A bowling ball falls faster than a feather in Earth’s atmosphere due to the feather’s higher air resistance relative to its weight.

Key Equations and Concepts

1. Distance Fallen Over Time:d=1/2 gt2 .
2. Terminal Velocity:
   • In real-world conditions, objects reach a maximum falling speed (terminal velocity) when air resistance balances the force of gravity.  This is why rain does not kill you.
3. Galileo’s Discovery:
   • Galileo showed that objects fall at the same rate regardless of their weight, overturning Aristotle’s earlier belief that heavier objects fall faster.

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