Free Fall

Motion
definition

Also known as: falling, gravitational acceleration

Grade 9-12

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Motion under gravity alone, with no air resistance — all objects in free fall accelerate at g \approx 9.81 m/s² regardless of mass. Free fall is the foundation for understanding projectile motion, orbital mechanics, and gravitational acceleration.

Definition

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

💡 Intuition

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

🎯 Core Idea

Gravity gives the same acceleration to all objects in a vacuum, regardless of mass.

Example

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

Formula

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

Notation

g \approx 9.81 m/s² is the acceleration due to gravity near Earth's surface, v_0 is the initial velocity, v is the velocity at time t, and y is the vertical position.

🌟 Why It Matters

Free fall is the foundation for understanding projectile motion, orbital mechanics, and gravitational acceleration. It explains why astronauts float in the space station (they are in continuous free fall), how parachutes work, and how Galileo overturned centuries of wrong thinking about falling objects.

💭 Hint When Stuck

When solving a free-fall problem, set the acceleration to g = 9.8 m/s² (or 10 m/s² if told to approximate). Choose a sign convention (e.g., downward = positive). Then apply the kinematic equations: v = v_0 + gt and d = v_0 t + \frac{1}{2}gt^2. For objects thrown upward, the initial velocity is positive and g acts opposite to motion.

Formal View

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

🚧 Common Stuck Point

Heavier objects fall at the same rate as lighter ones (ignoring air).

⚠️ 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.
  • 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.
  • Using the wrong sign for g — if you define 'up' as positive, then g should be negative (-9.8 m/s²); mixing up signs is the most common source of errors.

Frequently Asked Questions

What is Free Fall in Physics?

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

What is the Free Fall formula?

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

When do you use Free Fall?

When solving a free-fall problem, set the acceleration to g = 9.8 m/s² (or 10 m/s² if told to approximate). Choose a sign convention (e.g., downward = positive). Then apply the kinematic equations: v = v_0 + gt and d = v_0 t + \frac{1}{2}gt^2. For objects thrown upward, the initial velocity is positive and g acts opposite to motion.

Prerequisites

acceleration

How Free Fall Connects to Other Ideas

To understand free fall, you should first be comfortable with acceleration. Once you have a solid grasp of free fall, you can move on to projectile motion and gravity.

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