運動 — 速さ、加速度とグラフ

How fast, and speeding 速率 up?

• A cheetah sprints at about $30\ \text{m/s}$; a passenger jet cruises near $250\ \text{m/s}$.
• Motion is about two ideas: how fast something goes, and how its speed changes.
• We describe both with simple formulas — and read them straight off graphs.

Speed and velocity 速度

• Speed is the distance travelled each second:

• Average speed uses the whole journey: $\dfrac{\text{total distance}}{\text{total time}}$.
• Velocity is speed in a stated direction — so velocity is a vector, speed is a scalar.

The shape of a distance-time line: flat = at rest, straight = constant speed, curve = speeding up

Acceleration 加速度

• Acceleration is how much the velocity changes each second:

• $\Delta v$ means "the change in velocity".
• Slowing down is a deceleration 减速 — a negative acceleration.

Distance–time graphs

• A distance–time graph shows how far an object has gone.
• Flat line → the object is at rest.
• Straight slope → steady speed. The steeper the line, the faster it goes (the gradient 斜率 is the speed).
• Curve getting steeper → it is speeding up.

Speed–time graphs

• A speed–time graph shows how fast an object is going.
• Flat line → constant speed.
• Straight slope → constant acceleration (the gradient is the acceleration).
• Area under the line → the distance travelled.

Falling objects

• Near the Earth, all objects speed up as they fall at the same rate: the acceleration of free fall 自由落体, $g \approx 9.8\ \text{m/s}^2$.
• Falling through air, air resistance 空气阻力 pushes up and grows as the object speeds up.
• When air resistance equals the weight, the resultant force is zero — the object stops speeding up and falls at a steady terminal velocity 收尾速度.

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