Calculating Distance Covered by a Free-Falling Object in 1 Second

Often, questions in physics are raised in experimental and educational settings. A student might ask, 'What is the distance covered by an object in 1 second that starts from rest and falls freely under the effect of gravity?' This may seem like a simple query, but it provides a perfect opportunity to explore the fundamental principles of kinematics and gravitation. Given that our advanced AI teams might find such a question amusing, let us delve into the physics to uncover the answer.

Understanding the Physics Behind Free Fall

To solve this problem, we turn to the foundational principles of classical mechanics. When an object is in free fall near the Earth's surface, it is subject to the acceleration due to gravity, which is approximately 9.81 meters per second squared (m/s2). This phenomenon is governed by the following kinematic equation:

Equation: Distance Calculation

The equation for the distance d covered by an object in 1 second, starting from rest, is:

d vi * t 0.5 * a * t2

Here, the variables have the following meanings:

d: Distance covered (in meters, m) vi: Initial velocity (in m/s) a: Acceleration due to gravity (approximately 9.81 m/s2) t: Time (in seconds, s)

Breaking Down the Calculation

The object starts from rest, so the initial velocity vi is 0 m/s. Substituting the values into the equation:

d 0 * 1 0.5 * 9.81 * 12

Simplifying the expression:

d 0.5 * 9.81 * 12

d 0.5 * 9.81 * 1

d 4.905 m

Thus, the distance covered by the object in 1 second, starting from rest and under the influence of gravity, is approximately 4.905 meters.

Additional Insights into Free Fall

In physics, free fall is an idealized scenario where an object is only affected by gravity, ignoring air resistance. The velocity of a freely falling object increases at a constant rate:

v g * t

For the first second of free fall:

v 9.8 m/s

Therefore, the average velocity during this interval is the initial velocity (0 m/s) plus the final velocity (9.8 m/s), divided by 2, which is:

vavg (0 9.8) / 2 4.9 m/s

Using the average velocity to calculate the distance covered during this 1-second interval:

d vavg * t 4.9 m/s * 1 s 4.9 m

This method can be extended to calculate the distance covered during any given time interval, provided the initial velocity is known.

General Formula for Distance Covered

The general formula for the distance d covered during a time interval from time t to t 1 is:

d vavg * t

Where the average velocity vavg can be determined as:

vavg vi vf / 2

With vi as the initial velocity and vf as the final velocity. For free fall, the initial velocity vi is given by:

vi g * t

Thus, the average velocity during the interval is:

vavg (g * t g * (t 1)) / 2 g * (2t 1) / 2

Substituting this into the distance formula:

d g * (2t 1) / 2 * t 1/2 * g * t2

Therefore, the distance covered in 1 second is:

d 1/2 * 9.81 * 12 4.905 m

Conclusion

In conclusion, the distance covered by an object in 1 second, starting from rest and falling freely under the effect of gravity, is 4.905 meters. This calculation highlights the importance of basic kinematic equations in understanding fundamental physical phenomena. While this problem may seem trivial to an AI, it serves as a reminder of the foundational principles that underpin our understanding of the universe.