An object changes its speed when a force acts on it. As an extension of middle-school science, let us learn about the relationship between force and motion.
Basic Knowledge
Motion in which speed changes over time because a force acts is called accelerated motion.
The change in speed per second is called acceleration a, and its unit is m/s².
Uniformly accelerated linear motion:
・Speed: v = v0 + at (v₀:initial speed)
・Distance: s = v0t + (1/2)at²
Free fall: Motion in which an object initially at rest falls only under gravity. If air resistance is ignored, all objects fall with the same acceleration(approximately g = 9.8 m/s² on Earth).
Thus, the speed increases by 9.8m/s every second: 9.8m/s after 1 second, 19.6m/s after 2 seconds, and 29.4m/s after 3 seconds.
Acceleration a（Change in speed per unit of time. m/s²）
Uniformly accelerated motion（Motion with constant acceleration）
Free fall（Motion of falling from rest under gravity alone）
Gravitational acceleration g（Acceleration during free fall. 9.8 m/s² on Earth）
Equation of motion（F = ma. Force = mass × acceleration. Newton's second law）
Air resistance（Force exerted by air that obstructs an object's motion. It depends on speed）
Further Study (Background・Significance)
Galileo showed that heavy and light objects fall at the same time from the Leaning Tower of Pisa(legend). This overturned Aristotle's common belief that heavy objects fall faster.
In an environment with air, a light feather falls slowly because of air resistance, but in a vacuum container without air, a feather and an iron ball fall at the same time. This was demonstrated in the Apollo 15 lunar experiment(1971).
The equation of motion F = ma is the core of Newton's second law and connects force, mass, and acceleration. Even with the same force, a larger mass produces a smaller acceleration(the heavier an object is, the harder it is to move).
In free fall, distance = (1/2)gt², so an object falls 4.9m after 1 second, 19.6m after 2 seconds, and 44.1m after 3 seconds. Note that falling distance is proportional to the square of time.
Parachutes, skydiving, and the terminal velocity of raindrops are examples involving air resistance.
- Acceleration a = change in speed / time
- Uniform acceleration:
v = v0 + at - Acceleration of free fall g = 9.8 m/s²
- Free fall: 4.9m after 1 second, 19.6m after 2 seconds...
- Equation of motion F = ma (Newton's second law)
- Without air, objects fall at the same time regardless of their weight
- Distance = (1/2)gt² (proportional to the square of time)
Points to Note (Common Confusions)
① Change in speed and acceleration are different. Acceleration is the change in speed per unit of time. ② In free fall, all objects have the same acceleration regardless of weight(when air resistance is ignored). ③ The slope of a v-t graph is acceleration, and the enclosed area is distance. ④ Distance is proportional to the square of time, so doubling the time makes the distance four times greater.
Practice
- Approximately what is the gravitational acceleration on Earth in m/s²?
- Find the speed 3 seconds after an object falls freely from rest(g=9.8m/s²).
- Write Newton's equation of motion.