Free fall

Drop a hammer and a feather on the Moon and they land together — Apollo 15 actually did it. Free fall is the purest example of constant acceleration you'll ever meet, and you already own every tool it needs.

g: gravity as an acceleration

Near Earth's surface, every object in free fall accelerates downward at

$g \approx 9.81 \text{ m/s}^2$

regardless of its mass. Heavy things are pulled harder, but they're exactly that much harder to accelerate — the two effects cancel perfectly (the second law makes this precise in module 3). What actually separates the hammer from the feather on Earth is air resistance, not gravity.

The signature of falling

Watch a dropped ball with a strobe light — snapshots at equal time steps:

The gaps grow as 1 : 3 : 5 : 7 — Galileo's discovery. That odd-number pattern is exactly what x = ½gt² predicts: total distance after 1, 2, 3, 4 ticks is 1, 4, 9, 16 units, so each new gap is the difference between consecutive squares. When you see growing gaps like these, you're looking at constant acceleration.

Throwing upward

Throw a ball straight up at 20 m/s and gravity drains its speed by 9.81 m/s each second: 20, 10.2, 0.4… it stalls near t ≈ 2 s, then the same numbers replay in reverse on the way down. The flight is symmetric:

• Time up = time down.
• It lands at the same speed it left your hand (just pointed down).
• At the very top, velocity is zero — but the acceleration is still g. The ball isn't "done"; it's mid-turnaround.

That last point is the classic exam trap: zero velocity does not mean zero acceleration.

Why this matters

Free fall is the vertical half of every projectile. Next lesson we bolt on a horizontal motion — and discover that it changes nothing about the fall.