What is the effect of increasing speed on the distance traveled by a free-falling object?

When considering the motion of a free-falling object, it's important to recognize that the object accelerates due to gravity as it falls. In a vacuum, where air resistance is negligible, the acceleration due to gravity is constant at approximately 9.8 m/s².

As the object's speed increases while it falls, it covers more distance in each subsequent second. The distance fallen after a certain amount of time is not linear; rather, it follows a quadratic relationship with time due to the constant acceleration. Specifically, the equation that describes the distance ( s ) fallen after time ( t ) is:

[ s = \frac{1}{2} g t^2 ]

As time increases, the distance ( s ) increases quadratically with respect to time due to the cumulative effect of the increasing speed. Therefore, as the speed of the object increases, the distance it travels also increases. This reinforces the notion that with greater speed, more distance is covered over the same interval of time, confirming that distance indeed increases with speed for a free-falling object.