Understanding the Velocity of a Falling Object: From Rest to Motion

Introduction to Velocity and Acceleration

In the realm of physics and engineering, understanding the motion of objects under the influence of gravity is fundamental. This article explores the concept of velocity, particularly when an object falls from rest under the acceleration due to gravity. We'll delve into the mathematical formulations and physical implications of this phenomenon.

Acceleration Due to Gravity

Near the surface of the Earth, an object in free fall in a vacuum will accelerate at a constant rate due to gravity. This acceleration is approximately 9.8 m/s2. The equation to calculate the velocity of a freely falling object is given by: v u gt

where:

v is the final velocity of the object, u is the initial velocity (in this case, 0 m/s for an object falling from rest), g is the acceleration due to gravity (9.8 m/s2), and t is the time elapsed.

Calculating Velocity After 1 Second

Let's apply the formula to find the velocity of a stone that falls from rest from the top of a high tower:

Given values: Initial velocity, u 0 m/s (since the stone is from rest), Acceleration due to gravity, g 9.8 m/s2, and Time elapsed, t 1 s. Using the formula: v u gt 0 m/s 9.8 m/s2 × 1 s 9.8 m/s

This means that after 1 second, the velocity of the falling stone is 9.8 m/s.

Calculating Velocity After 2 Seconds

Now, let's calculate the velocity after 2 seconds using the same formula:

Given values: Initial velocity, u 0 m/s (since the stone is from rest), Acceleration due to gravity, g 9.8 m/s2, and Time elapsed, t 2 s. Using the formula: v u gt 0 m/s 9.8 m/s2 × 2 s 19.6 m/s

Thus, the velocity of the falling stone after 2 seconds is 19.6 m/s.

Terminal Velocity

While the stone is in free fall, it will accelerate until the force of air resistance equals the gravitational force. Once this occurs, the object reaches terminal velocity. For a human skydiver, the terminal velocity is approximately 53 m/s (190 km/h or 118 mph).

It's important to note that air resistance is negligible in our initial examples, but in real-world scenarios, it plays a significant role, especially in practical applications such as skydiving or designing falling objects for safety engineering.

Conclusion

The velocity of a falling object from rest, influenced by gravity, is a fundamental concept in physics. By understanding the acceleration due to gravity, and applying basic kinematic equations, one can accurately predict the motion of objects in free fall. This knowledge is essential in a variety of fields, from engineering to sports science.