If a free-falling ball is equipped with a speedometer, by how much would its speed reading increase for every second?

1. Break Down the Problem

To find the increase in speed of a free-falling ball each second, we need to focus on the concept of acceleration due to gravity.

2. Relevant Concepts

The primary concept is the acceleration of a freely falling object under the influence of gravity. In the absence of air resistance, all objects accelerate towards the Earth at approximately $9.81 \, \text{m/s}^2$.

3. Analysis and Detail

When an object is in free fall, it gains speed continuously as it falls. The speed increases by the gravitational acceleration each second:

• Initial speed ($v_0$): 0 m/s (when dropped)
• Speed increase each second: $g = 9.81 \, \text{m/s}^2$

So, for every second that the ball falls, its speed increases by $9.81 \, \text{m/s}$.

4. Verify and Summarize

The calculation shows that the speed increases at a constant rate due to gravitational acceleration, verifying that the assumptions are correct and consistent with known physics.

Final Answer

The speed reading of the free-falling ball increases by $9.81 \, \text{m/s}$ for every second it falls.