Distance Travelled In Free Fall Under Gravity Given Initial Velocity And Time Calculator

Distance Travelled Formula:

\[ d_f = u \cdot t + \frac{1}{2} \cdot g \cdot t^2 \]

Distance Travelled (d_f):

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1. What is Distance Travelled in Free Fall?

Distance Travelled in Free Fall refers to an object's overall change in position when falling under the influence of gravity, accounting for both its initial velocity and the acceleration due to gravity over time.

2. How Does the Calculator Work?

The calculator uses the distance travelled formula:

\[ d_f = u \cdot t + \frac{1}{2} \cdot g \cdot t^2 \]

Where:

\( d_f \) — Distance travelled in free fall (meters)
\( u \) — Initial velocity (m/s)
\( t \) — Time (seconds)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The equation calculates the total distance an object travels during free fall, combining the distance covered due to initial velocity and the distance gained from gravitational acceleration.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for physics applications, engineering designs, safety calculations, and understanding motion under gravitational influence.

4. Using the Calculator

Tips: Enter initial velocity in m/s and time in seconds. Time must be a non-negative value. The calculator uses standard gravitational acceleration of 9.80665 m/s².

5. Frequently Asked Questions (FAQ)

Q1: What if the initial velocity is zero?
A: If initial velocity is zero, the formula simplifies to \( d_f = \frac{1}{2} \cdot g \cdot t^2 \), which represents distance travelled from rest under gravity.

Q2: Does this formula account for air resistance?
A: No, this formula assumes ideal free fall conditions without air resistance. For real-world applications with significant air resistance, more complex models are needed.

Q3: Can this be used for upward motion?
A: Yes, but with appropriate sign conventions. For upward motion, initial velocity would be positive while acceleration due to gravity is negative.

Q4: What is the value of gravitational acceleration used?
A: The calculator uses standard gravitational acceleration on Earth: 9.80665 m/s².

Q5: How accurate is this calculation for real-world scenarios?
A: This provides theoretical values for ideal conditions. Real-world factors like air resistance, altitude variations, and local gravitational differences may affect actual results.