Calculate the final velocity and total distance fallen of an object dropped from rest in a vacuum. Gravity is assumed to be 9.80665 m/s².
Final Velocity (v)
49.033m/s
Distance Fallen (d)
122.583m
Distance vs 10s Fall (490.3m)
How is this calculated?
1. Velocity: v = g × t
v = 9.80665 × 5 = 49.033 m/s
2. Distance: d = ½ × g × t²
d = 0.5 × 9.80665 × 5² = 122.583 m
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About the Free Fall Calculator
Understanding how fast objects fall is a fundamental concept in physics. This calculator helps you determine the exact velocity and total distance fallen for an object dropped from rest in a vacuum. By stripping away air resistance, true free fall provides an elegant view of gravity's constant effect, demonstrating principles famously established by Galileo and confirmed by astronauts on the moon.
Mathematical Formula & Logic
The calculator uses standard kinematic equations. Assuming an object starts from rest and is only influenced by Earth's gravity, its velocity increases continuously by 9.80665 m/s every second. The distance fallen accelerates exponentially.
1. Final Velocity:
v = g × t
Where:
- v = final velocity in metres per second (m/s)
- g = acceleration due to gravity (9.80665 m/s² on Earth)
- t = time of fall in seconds (s)
2. Distance Fallen:
d = ½ × g × t²
Where:
- d = distance fallen in metres (m)
Step-by-Step Example
Calculate the final velocity and distance an object falls after exactly 3 seconds:
Step 1 — find the velocity
1. Known: t = 3 s, g = 9.80665 m/s²
2. Apply v = g × t
3. v = 9.80665 × 3 = 29.420 m/s
Step 2 — find the distance fallen
4. Apply d = ½ × g × t²
5. d = 0.5 × 9.80665 × 3²
6. d = 0.5 × 9.80665 × 9 = 44.130 m
After 3 seconds, the object is travelling downwards at 29.420 m/s and has fallen 44.130 metres.
Reference Data & Values
time seconds
velocity m_s
distance m
1
9.807
4.903
2
19.613
19.613
3
29.420
44.130
5
49.033
122.583
10
98.067
490.333
Frequently Asked Questions
No. In a vacuum, all objects fall at exactly the same rate regardless of their mass. This was famously demonstrated by Galileo, and later by astronauts on the moon dropping a hammer and a feather. The effect of mass cancels out between inertial resistance and gravitational force.
Terminal velocity occurs in the real world when the upward force of air resistance equals the downward force of gravity, stopping the object from accelerating further. This calculator assumes a vacuum where terminal velocity is never reached.
The distance fallen from rest is calculated as d = 1/2 * g * t^2, where g is standard gravity (9.80665 m/s^2) and t is time in seconds.
The standard acceleration due to gravity on Earth is 9.80665 m/s². It can vary slightly depending on your altitude and latitude, but this constant is universally used for typical calculations.
To find the final velocity of an object in free fall from rest, multiply the acceleration due to gravity (9.80665 m/s²) by the time it has been falling in seconds.
Air resistance opposes the motion of a falling object, reducing its acceleration until it reaches terminal velocity. Aerodynamic and light objects feel this effect much sooner than dense, heavy objects.
True free fall (without air resistance) is only possible in a vacuum chamber on Earth, though for short drops of heavy, aerodynamic objects (like a steel ball bearing), the effect of air is so negligible that free fall kinematics apply accurately.
In an ideal free fall, acceleration remains constant at approximately 9.8 m/s², while the velocity increases steadily every second by that exact amount.