The speed of a falling rock is not fixed; it constantly changes as the object travels toward the ground. Gravity causes the rock to gain speed throughout its descent, a process known as acceleration. To understand the rock’s speed, one must first consider the theoretical maximum speed it can achieve under the influence of gravity alone, defining a state called free fall. This theoretical approach provides the groundwork before considering the real-world forces that modify the speed of any object falling through Earth’s atmosphere.
The Constant Rate of Speed Change
The fundamental driver of a rock’s fall is the acceleration caused by Earth’s gravity, which is a near-constant value close to the planet’s surface. This rate of speed change is approximately 32 feet per second squared (32 ft/s²). This means that for every second the rock is in free fall, its downward velocity increases by an additional 32 feet per second.
If a rock is dropped from a standstill, after one second, its speed will be about 32 feet per second. After two seconds, the speed will increase to 64 feet per second, and after three seconds, it will reach 96 feet per second.
This continuous, uniform addition to the velocity defines constant acceleration. This holds true regardless of the rock’s mass, assuming no other forces are involved.
Factors That Affect the Fall Speed
While gravitational acceleration is constant, the actual speed of a falling rock is significantly influenced by the presence of air. As the rock drops, it encounters air resistance, a type of fluid friction acting upward against the motion. This resistance is not constant; its magnitude increases as the rock’s speed increases.
This opposing force reduces the net downward force acting on the rock, causing the actual acceleration to be less than the theoretical 32 ft/s². Air resistance is also affected by the rock’s shape and surface area; a flat, irregular rock experiences more drag than a smooth, dense one of the same mass.
Eventually, if the rock falls far enough, the upward force of air resistance will exactly balance the downward force of gravity, resulting in a net force of zero. At this point, the rock stops accelerating and maintains a maximum, constant speed, known as terminal velocity.
Calculating the Rock’s Speed
For short falls where air resistance is minimal, the theoretical speed of the rock can be calculated using a simple relationship between velocity and time. The instantaneous speed (\(v\)) of a rock dropped from rest is estimated by multiplying the gravitational acceleration (\(g\)) by the time (\(t\)) it has been falling (\(v = g \times t\)). For example, after 0.25 seconds, the speed would be approximately 32 ft/s² × 0.25 s, which equals 8 feet per second.
The total distance (\(d\)) the rock has fallen can be calculated using the formula \(d = 1/2 \times g \times t^2\). Using the same 0.25 second time frame, the rock would have traveled about 1 foot.
These calculations provide an accurate prediction for the motion of a rock over short distances, such as dropping it from a few stories high. This is valid before the effects of air resistance become substantial enough to require more complex modeling.