Free Fall Formula

Motion under gravity alone, with no air resistance — all objects in free fall accelerate at g approximately 9.81 m/s² regardless of mass.

The Formula

v=v0+gt;d=12gt2v = v_0 + gt \quad ; \quad d = \frac{1}{2}gt^2

When to use: A dropped ball accelerates at the same rate regardless of its mass.

Quick Example

On Earth, objects fall with a=g≈9.8 m/s2a = g \approx 9.8 \text{ m/s}^2 (or 10 m/s210 \text{ m/s}^2 approximation).

Notation

g≈9.81g \approx 9.81 m/s² is the acceleration due to gravity near Earth's surface, v0v_0 is the initial velocity, vv is the velocity at time tt, and yy is the vertical position.

What This Formula Means

Motion under gravity alone, with no air resistance — all objects in free fall accelerate at g≈9.81g \approx 9.81 m/s² regardless of mass.

A dropped ball accelerates at the same rate regardless of its mass.

Formal View

In free fall near Earth's surface, a⃗=−gj^\vec{a} = -g\hat{j} where g≈9.81g \approx 9.81 m/s². The kinematic equations become y=y0+v0t−12gt2y = y_0 + v_0 t - \frac{1}{2}gt^2 and v=v0−gtv = v_0 - gt (taking upward as positive). The time to fall from height hh from rest is t=2h/gt = \sqrt{2h/g}.

Worked Examples

Example 1

easy
A stone is dropped from a cliff. How far does it fall in 3 s3 \text{ s}? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Answer

d=44.1 md = 44.1 \text{ m}

First step

1
Initial velocity: v0=0v_0 = 0 (dropped from rest).

Full solution

  1. 2
    Use the free-fall displacement equation: d=v0t+12gt2d = v_0 t + \frac{1}{2}gt^2.
  2. 3
    d=0+12(9.8)(9)=44.1 md = 0 + \frac{1}{2}(9.8)(9) = 44.1 \text{ m}
In free fall, the only force acting is gravity. All objects fall at the same rate regardless of mass (ignoring air resistance), accelerating at g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 2

medium
A ball is thrown upward with an initial velocity of 20 m/s20 \text{ m/s}. How high does it go, and how long until it returns? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 3

medium
A stone is dropped from a 125 m125 \text{ m} tall cliff. Find its impact speed. Use g=10 m/s2g = 10 \text{ m/s}^2.

Common Mistakes

  • Thinking heavier objects fall faster — in the absence of air resistance, all objects fall at the same rate; a feather and a hammer dropped on the Moon land together. - Fix this by naming the system, checking "Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?", and attaching units or direction to the final statement.
  • Forgetting that an object thrown upward is still in free fall the entire time — gravity acts on it continuously, including at the very top where its velocity is momentarily zero. - Fix this by naming the system, checking "Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?", and attaching units or direction to the final statement.
  • Using the wrong sign for gg — if you define 'up' as positive, then gg should be negative (−9.8-9.8 m/s²); mixing up signs is the most common source of errors. - Fix this by naming the system, checking "Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?", and attaching units or direction to the final statement.
  • Using free fall from a keyword alone - Signal words like position, speed, velocity only point to a possible model; the system must match too.

Why This Formula Matters

Free Fall helps students describe motion precisely instead of relying on everyday words like fast or slow. It prepares them to interpret graphs, choose equations, and connect motion to forces and energy.

Frequently Asked Questions

What is the Free Fall formula?

Motion under gravity alone, with no air resistance — all objects in free fall accelerate at g≈9.81g \approx 9.81 m/s² regardless of mass.

How do you use the Free Fall formula?

A dropped ball accelerates at the same rate regardless of its mass.

What do the symbols mean in the Free Fall formula?

g≈9.81g \approx 9.81 m/s² is the acceleration due to gravity near Earth's surface, v0v_0 is the initial velocity, vv is the velocity at time tt, and yy is the vertical position.

Why is the Free Fall formula important in Physics?

Free Fall helps students describe motion precisely instead of relying on everyday words like fast or slow. It prepares them to interpret graphs, choose equations, and connect motion to forces and energy.

What do students get wrong about Free Fall?

Students often know a formula related to free fall but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Free Fall formula?

Before studying the Free Fall formula, you should understand: acceleration.

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