Free fall

Beginner

Motion under gravity alone, with acceleration about 9.8 m/s².

Key relationy = ½gt²

In free fall only gravity acts. All bodies accelerate downward at about 9.8 m/s² regardless of mass, because the weight and the inertia both scale with mass. The equations of constant acceleration apply with a = g.

Worked example

Dropped from rest, an object falls 4.9 m in 1 s and 19.6 m in 2 s.

Common mistake

Air resistance is ignored; a feather falls slowly in air but together with a hammer in a vacuum.

In more detail

In free fall, an object moves under gravity alone, with acceleration g of about 9.8 m/s² downward, and air resistance is ignored. The motion is uniformly accelerated and follows the standard equations.

How to solve it

Choose downward as positive, or upward as positive, and keep it consistent.
Set the initial velocity to zero if the object is dropped, and use a = g = 9.8 m/s².
Use v² = 2gh to find the impact speed from the height, or h = ½gt² to find the time.
Ignore air resistance unless the question asks for it or the object is very light or fast.

Worked examples

Example 1: A stone is dropped from a height of 20 m. How long does it take to hit the ground, and how fast is it moving?

Time: h = ½gt², so t = sqrt(2h/g) = sqrt(40/9.8) = 2.02 s. Speed: v = sqrt(2gh) = sqrt(2 × 9.8 × 20) = sqrt(392) = 19.8 m/s.

Example 2: A stone is dropped from rest. How fast is it moving after 3 s, and how far has it fallen?

v = gt = 9.8 × 3 = 29.4 m/s. Distance: s = ½gt² = ½ × 9.8 × 9 = 44.1 m.

Checking your answer

Free-fall speed grows by about 9.8 m/s every second. After 3 s the speed should be roughly 30 m/s, which matches 29.4 m/s.

Real-world uses

Estimating how long a dropped phone takes to hit the ground.
Designing emergency drop tests for packaging.
Stunt planners calculate how far a stuntperson falls from a height before the mat, to decide how far it needs to extend.

Open the interactive lesson, with simulation and quiz →

Frequently asked questions

Does mass affect free-fall acceleration?

No. In a vacuum, all objects fall with the same acceleration.

Is an object in free fall weightless?

Yes, in the sense that it feels no contact force, because it is accelerating with gravity.

Does a heavier object fall faster?

No. In free fall without air resistance, all objects accelerate at the same rate, so a heavier object does not fall faster.