Home › Articles › Kinematics › Free Fall and Gravity
Free Fall and Gravity
Kinematics
Drop a stone and a feather in a vacuum and they hit the ground together. That surprising fact is the heart of free fall: near Earth's surface, gravity accelerates every object at the same rate, regardless of its mass. This article explains what free fall is, the equations that describe it, and why air resistance changes what we see in everyday life.
What free fall is
An object is in free fall when gravity is the only force acting on it. Near Earth's surface, that means it accelerates downward at **g = 9.81 m/s²**, a value that is the same for a stone, a coin, or a bowling ball. The classic demonstration is a feather and a coin in a vacuum tube: with the air removed, they fall side by side. In everyday air, the feather falls slowly because air resistance pushes up on it — but that is not free fall, because a second force is acting. Free fall is an idealisation, but a very useful one for falling objects over short distances.
The equations of free fall
Free fall is motion with constant acceleration g, so the SUVAT equations apply with a = g. Dropped from rest, an object reaches velocity **v = g t** after t seconds and falls a distance **s = ½ g t²**. After 1 s it is moving at about 9.81 m/s and has fallen about 4.9 m; after 2 s it is moving at about 19.6 m/s and has fallen about 19.6 m. Notice the distance grows with the square of the time, so the second second of falling covers far more ground than the first. If the object is thrown downward or upward, use the full SUVAT equations with u as the initial velocity.
Air resistance and terminal velocity
In real air, a falling object feels air resistance (drag) pushing upward, and that drag grows as the object speeds up. Eventually the drag can balance the weight, the net force becomes zero, and the object stops accelerating and falls at a steady speed called **terminal velocity**. A skydiver reaches a terminal velocity of roughly 53 m/s in a spread-eagle position, and much faster head-down. A feather reaches its terminal velocity almost immediately because its weight is tiny compared with the drag on its large surface, which is why it drifts down so slowly.
📝 Worked example: dropping a stone
A stone is dropped from rest from a cliff. Ignore air resistance and use g = 9.81 m/s². After 3 s, velocity v = g t = 9.81 x 3 = 29.43 m/s. Distance fallen s = 1/2 g t² = 0.5 x 9.81 x 3² = 0.5 x 9.81 x 9 = 44.145 m. Answer: after 3 s the stone is falling at 29.43 m/s and has fallen about 44.1 m.
Common mistakes
- Thinking heavier objects fall faster. Correction: in free fall all objects accelerate at g; heavier objects only seem to fall faster in air because air resistance affects them less relative to their weight.
- Using g = 10 without checking the question. Correction: use g = 9.81 m/s² unless the question says to use 10 — the difference changes the answer.
- Forgetting that free fall assumes no air resistance. Correction: for light objects or long falls, drag matters and the SUVAT free-fall answers will be too large.
Practice questions
- A ball is dropped from rest. How fast is it moving after 2 s? Use g = 9.81 m/s².
Show answer
v = g t = 9.81 x 2 = 19.62 m/s downward.
- How far does an object dropped from rest fall in 4 s? Ignore air resistance.
Show answer
s = 1/2 g t² = 0.5 x 9.81 x 16 = 78.48 m.
- A coin and a feather are dropped together inside a vacuum chamber. Which lands first?
Show answer
They land together — with no air resistance, both accelerate at g and fall the same distance in the same time.
Frequently asked questions
Is the Moon in free fall?
Yes. The Moon is constantly falling toward Earth under gravity, but its sideways motion keeps it in orbit instead of hitting the ground.
Does g change with height?
Slightly — g gets smaller as you go higher above Earth, but near the surface the change is tiny and 9.81 m/s² is a good value.