Understanding the Distance Covered by a Free-Falling Body in the First Second

Introduction

The concept of a free-falling body, starting from rest (0 velocity), and the distance it covers in one second might be counterintuitive. This article will clarify the formula used to calculate this distance and address any misconceptions. Specifically, we will explore the correct distance covered by a free-falling body in the first second, which is approximately 5 meters, not 10 meters as often mistakenly believed.

The Formula for Free-Fall

The formula for the distance a body covers under the influence of gravity, starting from rest, is given by:

S 0.5 * g * t2

Where:

S is the distance covered (in meters, m) g is the acceleration due to gravity (9.806 m/s2) t is the time (in seconds, s)

Calculation for One Second

Substituting the values g 9.806 m/s2 and t 1 second into the formula, we get:

S 0.5 * 9.806 * (1)2

S 4.903 meters

This means that a body starting from rest will cover approximately 4.903 meters in the first second under the influence of gravity. This is precisely where the common misconception arises. Many people assume that, due to the value 9.806, the distance must be close to 10 meters, but in reality, it is only about 5 meters.

Initial Velocity Considerations

However, it is important to note that if the object is projected downward with an initial velocity V0, the formula for the distance covered changes to:

S V0 * t 0.5 * g * t2

For an initial velocity of 5 m/s, the distance covered in the first second would be:

S 5 * 1 0.5 * 9.806 * (1)2

S ≈ 7.453 meters

This demonstrates that the initial velocity significantly affects the distance covered by the body. When there is no initial velocity (starting from rest), the distance covered in the first second is approximately 4.903 meters, not 10 meters.

Conclusion

Understanding the distance covered by a free-falling body in the first second involves correctly applying the formula S 0.5 * g * t2. This article has shown that the commonly mistaken distance is much less than 10 meters, at approximately 5 meters when starting from rest. The inclusion of an initial velocity can alter the distance, but the base value remains around 4.903 meters for an object starting from rest.

Keywords: free falling distance, gravitational acceleration, initial velocity