Motion — speed, acceleration and graphs · 运动——速率、加速度与图
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| speed/spiːd/ | 速率 | sù lǜ |
| velocity/vəˈlɒsɪti/ | 速度 | sù dù |
| acceleration/əkˌseləˈreɪʃn/ | 加速度 | jiā sù dù |
| deceleration/dɪˌseləˈreɪʃn/ | 减速 | jiǎn sù |
| gradient/ˈɡreɪdɪənt/ | 斜率 | xié lǜ |
| free fall/friː fɔːl/ | 自由落体 | zì yóu luò tǐ |
| air resistance/eə rɪˈzɪstəns/ | 空气阻力 | kōng qì zǔ lì |
| terminal velocity/ˈtɜːmɪnl vəˈlɒsɪti/ | 收尾速度 | shōu wěi sù dù |
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.
多快,以及在加速?
- 一只猎豹以大约 $30\ \text{m/s}$ 冲刺;一架客机以接近 $250\ \text{m/s}$ 巡航。
- 运动关乎两个想法:某物走得多快,以及它的速率如何变化。
- 我们用简单的公式描述两者——并直接从图上读出它们。
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
速率和速度
- 速率(speed)是每秒走过的距离:
- 平均速率使用整个旅程:$\dfrac{\text{total distance}}{\text{total time}}$。
- 速度(velocity)是一个陈述方向上的速率——所以速度是一个矢量,速率是一个标量。
一条距离-时间线的形状:平 = 静止,直 = 恒定速率,曲线 = 在加速
Speed, acceleration & graphs · 速率、加速度与图
v = u + at
On a speed–time graph the gradient is the acceleration and the area · 面积 underneath is the distance travelled. · 在一张速率–时间图上,斜率是加速度而下面的面积是走过的距离。
A runner covers $100\ \text{m}$ in · 入 $8.0\ \text{s}$. What is the average speed, in m/s? · 一个跑步者在 $8.0\ \text{s}$ 内走过 $100\ \text{m}$。平均速率是多少,以 m/s 计?
$v = \dfrac{s}{t} = \dfrac{100}{8.0} = 12.5\ \text{m/s}$. · $v = \dfrac{s}{t} = \dfrac{100}{8.0} = 12.5\ \text{m/s}$。
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.
加速度
- 加速度(acceleration)是速度每秒变化多少:
- $\Delta v$ 意思是"速度的变化"。
- 减速是一个减速度(deceleration)——一个负的加速度。
A car speeds up from rest to $20\ \text{m/s}$ in · 入 $4.0\ \text{s}$. What is its acceleration, in m/s²? · 一辆车从静止在 $4.0\ \text{s}$ 内加速到 $20\ \text{m/s}$。它的加速度是多少,以 m/s² 计?
$a = \dfrac{\Delta v}{\Delta t} = \dfrac{20 - 0}{4.0} = 5.0\ \text{m/s}^2$. · $a = \dfrac{\Delta v}{\Delta t} = \dfrac{20 - 0}{4.0} = 5.0\ \text{m/s}^2$。
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.
距离–时间图
- 一张距离–时间图显示一个物体走了多远。
- 平线 → 物体静止。
- 直斜坡 → 稳定的速率。线越陡,它走得越快(斜率是速率)。
- 曲线变得更陡 → 它在加速。
On a distance–time graph, a flat (horizontal) line means the object is: · 在一张距离–时间图上,一条平(水平)线意味着物体:
A flat distance–time line means the distance is not changing — the object is at rest. · 一条平的距离–时间线意味着距离没有变化——物体静止。
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.
速率–时间图
- 一张速率–时间图显示一个物体走得多快。
- 平线 → 恒定速率。
- 直斜坡 → 恒定加速度(斜率是加速度)。
- 线下的面积 → 走过的距离。
On a speed–time graph, the area under the line is the distance travelled. · 在一张速率–时间图上,线下的面积是走过的距离。
Speed × time = distance, and that is exactly the area under a speed–time line. · 速率 × 时间 = 距离,而那恰好是一条速率–时间线下的面积。
A car travels at a constant $10\ \text{m/s}$ for $6.0\ \text{s}$. From the speed–time graph (area), how far does it go, in m? · 一辆车以恒定的 $10\ \text{m/s}$ 行驶 $6.0\ \text{s}$。从速率–时间图(面积),它走多远,以 m 计?
The area is a rectangle: $10 \times 6.0 = 60\ \text{m}$. · 面积是一个矩形:$10 \times 6.0 = 60\ \text{m}$。
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.
下落的物体
- 在地球附近,所有物体下落时以相同的速率加速:自由落体加速度(acceleration of free fall),$g \approx 9.8\ \text{m/s}^2$。
- 在空气中下落,空气阻力(air resistance)向上推并随物体加速而增长。
- 当空气阻力等于重量时,合力为零——物体停止加速并以一个稳定的终端速度(terminal velocity)下落。
A skydiver reaches terminal velocity. This happens because: · 一个跳伞者达到终端速度。这发生因为:
As speed rises, air resistance grows until it balances the weight. The resultant force is then zero, so the speed stays steady. · 随着速率上升,空气阻力增长直到它平衡重量。合力于是为零,所以速率保持稳定。
You've got it
- speed $v = \dfrac{s}{t}$; velocity is speed with a direction
- acceleration $a = \dfrac{\Delta v}{\Delta t}$; slowing down is negative
- distance–time: gradient = speed · speed–time: gradient = acceleration, area = distance
- free fall: $g \approx 9.8\ \text{m/s}^2$; terminal velocity when air resistance = weight
你掌握了
- 速率 $v = \dfrac{s}{t}$;速度是带方向的速率
- 加速度 $a = \dfrac{\Delta v}{\Delta t}$;减速是负的
- 距离–时间:斜率 = 速率 · 速率–时间:斜率 = 加速度,面积 = 距离
- 自由落体:$g \approx 9.8\ \text{m/s}^2$;空气阻力 = 重量时终端速度