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Physics › Motion
Motion
Position, velocity, acceleration. Three layers of how things move — each the rate of change of the one above.
Falling ball
●
Time
0.00 s
Distance fallen
0.0 m
Velocity
0.0 m/s
Height left
50.0 m
d = ½gt² · v = gt · g ≈ 9.8 m/s²
The three layers
- Position — where you are.
- Velocity — how fast position is changing.
- Acceleration — how fast velocity is changing.
Free fall
Drop something near Earth's surface (and ignore air). It accelerates downward at g ≈ 9.8 m/s². After 1 second it's moving at 9.8 m/s and has fallen 4.9 m. After 2 seconds it's at 19.6 m/s and 19.6 m down. Velocity grows linearly; distance grows as a square.
The two formulas
From rest under constant acceleration:
velocity:
distance:
velocity:
v = g·tdistance:
d = ½·g·t²Why d grows like t²
Velocity is rising linearly with time — average velocity over an interval is half of the final. So distance equals average velocity times time, which gives the ½·g·t² formula. Calculus makes this rigorous: distance is the integral of velocity.