A Free Fall Acceleration Calculator is a physics-based tool that solves for various aspects of an object's motion when it is falling under the sole influence of gravity. This state is known as "free fall." The calculator uses the fundamental equations of motion, incorporating the constant acceleration due to gravity (g), to determine key variables such as the object's final velocity, the total distance it has fallen, or the total time of its fall. It is an essential resource for students learning physics, as well as for engineers and scientists who need to analyze the motion of falling objects in a simplified, ideal environment (without air resistance).
formula of Free Fall Acceleration Calculator
The calculations for free fall are based on the constant acceleration of gravity, a value represented by 'g'.
Standard Gravity (g): 9.80665 m/s² (meters per second squared) or 32.174 ft/s² (feet per second squared). For most calculations, you can approximate this to 9.8 m/s² or 32.2 ft/s².
1. Calculating Final Velocity (with Time)
This formula calculates an object's final speed after a certain amount of time has passed.
Formula:
Final Velocity (v) = Initial Velocity (v₀) + (g * Time (t))
- v: The final velocity of the object.
- v₀: The initial velocity. If the object is simply dropped, this value is 0.
- g: The acceleration due to gravity.
- t: The total time the object has been falling.
2. Calculating Distance Fallen
This formula calculates the total distance an object falls over a given time.
Formula:
Distance (d) = (Initial Velocity (v₀) * Time (t)) + (0.5 * g * Time (t)²)
- d: The distance the object has fallen.
- v₀: The initial velocity. If the object is dropped, this term becomes 0.
- g: The acceleration due to gravity.
- t: The time the object has been falling.
3. Calculating Final Velocity (with Distance)
This formula is useful when you know the distance an object has fallen but not the time.
Formula:
Final Velocity (v)² = Initial Velocity (v₀)² + (2 * g * Distance (d))
To solve for the final velocity, you take the square root of the result.
Formula (Solved for v):
Final Velocity (v) = sqrt(Initial Velocity (v₀)² + (2 * g * Distance (d)))
4. Calculating Time of Fall
If you know the distance an object has fallen and its initial velocity was zero, you can rearrange the distance formula to solve for time.
Formula (when dropped from rest):
Time (t) = sqrt((2 * Distance (d)) / g)
Free Fall from Rest: Quick Reference Table
This table shows the distance an object will fall and the velocity it will reach after each second, assuming it is dropped from rest (initial velocity = 0) and using g = 9.8 m/s².
| Time (seconds) | Distance Fallen (meters) | Final Velocity (m/s) |
| 1 | 4.9 m | 9.8 m/s |
| 2 | 19.6 m | 19.6 m/s |
| 3 | 44.1 m | 29.4 m/s |
| 4 | 78.4 m | 39.2 m/s |
| 5 | 122.5 m | 49.0 m/s |
Example of Free Fall Acceleration Calculator
Let's calculate the final velocity and time of fall for a stone dropped from a 50-meter-high cliff.
First, we identify the known values.
- Initial Velocity (v₀): The stone is dropped, so v₀ = 0.
- Distance (d): 50 meters.
- Acceleration of Gravity (g): We will use 9.8 m/s².
Step 1: Calculate the Time of Fall.
Since we know the distance and the initial velocity is 0, we can use the time of fall formula.
Time (t) = sqrt((2 * 50) / 9.8)
Time (t) = sqrt(100 / 9.8) ≈ 3.19 seconds
Step 2: Calculate the Final Velocity.
Now that we know the time, we can use the final velocity formula.
Final Velocity (v) = v₀ + (g * t)
Final Velocity (v) = 0 + (9.8 * 3.19) ≈ 31.26 m/s
Therefore, the stone will take approximately 3.19 seconds to hit the ground, and its velocity just before impact will be about 31.26 meters per second.
Most Common FAQs
No, these are the formulas for "ideal" free fall, which assumes the only force acting on the object is gravity. In the real world, air resistance (or drag) will oppose the motion of a falling object, slowing it down. This effect is more significant for lighter objects with a large surface area, like a feather, and less significant for dense, compact objects, like a steel ball.
In ideal free fall (without air resistance), the mass of the object does not affect its acceleration. A heavy object and a light object dropped from the same height at the same time will hit the ground simultaneously. This is a famous principle demonstrated by Galileo.
If an object is thrown downwards, it has a non-zero initial velocity (v₀). In this case, you must include the value of the initial velocity in the formulas. The object will reach the ground faster and with a higher final velocity than if it were simply dropped from the same height.