Kinematics
A-Level Physics Topic 2 20:32 English narration · English + 中文 subtitles burned in
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In 1971, an astronaut stood on the Moon and held out a hammer and a feather.
1971年，一位宇航员站在月球上，伸出一把锤子和一根羽毛。
On Earth, the feather would flutter down slowly, far behind the hammer.
在地球上，羽毛会缓缓飘落， 远远落在锤子后面。
But the Moon has no air.
但月球上没有空气。
He let them go at the very same moment.
他在同一时刻松开双手。
And they fell side by side, and touched the ground together.
它们并排下落， 同时触到地面。
With no air to slow it, every object falls at exactly the same rate.
没有空气减慢它们，每个物体都以完全相同的速率下落。
That is the heart of kinematics: describing how things move.
这就是运动学的核心：描述物体如何运动。
Today we learn the words, the graphs, and the equations of motion.
今天我们学习这些术语、这些图像， 以及运动方程。
Then we send objects flying through the air.
然后我们让物体在空中飞行。
Let's begin.
让我们开始吧。
Five words describe motion, and the examiner wants them exact.
五个词描述运动，考官要求用得精确。
Distance is the total path travelled — a scalar, size only.
距离是走过的总路程——一个标量，只有大小。
Displacement is the straight line from start to end, with a direction — a vector.
位移是从起点到终点的直线，带有方向——一个矢量。
Speed is how fast distance changes.
速率是距离变化的快慢。
Velocity is how fast displacement changes, so it carries a direction too.
速度是位移变化的快慢，所以它也带有方向。
And acceleration is how fast the velocity changes.
而加速度是速度变化的快慢。
Remember, deceleration is just acceleration pointing the other way.
记住，减速只是方向与速度相反的加速，并不是另一个量。
Keep the definitions exact — they score marks by wording alone.
把这些定义记准——仅靠措辞就能得分。
The unit of speed and of velocity is metres per second.
速率和速度的单位是米每秒。
The unit of acceleration is metres per second squared.
加速度的单位是 米每二次方秒。
A speedometer shows speed: how many metres of path you cover each second.
车速表显示的是速率：你每秒走过多少米的路程。
It does not know which way you face.
它不知道你朝哪边。
That is why speed is a scalar, while velocity must name a direction as well.
这就是为什么速率是标量，而速度还必须说明方向。
Two more phrases the examiner uses precisely.
还有两个考官用得很精确的说法。
Uniform acceleration means constant acceleration — a straight line on a velocity-time graph.
匀加速的意思是加速度恒定——在速度—时间图上是一条直线。
And the acceleration of free fall, g, is the acceleration of an object falling freely in a uniform gravitational field, with air resistance negligible.
而自由落体加速度 g，是物体在匀强重力场中自由下落时的加速度， 并且空气阻力可以忽略。
Negligible is the exam's way of saying you may take it as zero.
「可以忽略」是考试的说法，意思是你可以把它当作零。
Picture a walk that loops around a park and returns to the gate.
想象绕公园走一圈再回到大门。
The distance is the whole loop — every step you took.
距离是整圈——你迈出的每一步。
The displacement is zero, because start and end are the same place.
位移却是零， 因为起点和终点是同一个地方。
Average speed uses the loop length.
平均速率用整圈的长度。
Average velocity uses the displacement, so for a closed path it is also zero.
平均速度用位移， 所以对闭合路径它也是零。
Examiners love this trap: large distance, zero displacement.
考官很爱这个陷阱：很大的距离，零的位移。
A high-speed train on a long track is a clean real-world story for motion graphs.
高架桥上的高速列车，是运动图像最干净的现实故事。
You can plot how far it has gone against the clock, or how fast it is going against the clock.
你可以画出它走了多远对时间， 或它有多快对时间。
Many marks come from reading or drawing those two graphs.
许多分数来自读图或画这两类图。
Get the axes right first: the vertical quantity is what you measure, the horizontal is always time.
先把坐标轴弄对： 竖直方向是你要量的量，水平方向永远是时间。
Now the graphs.
现在看图像。
First, displacement against time.
首先是位移对时间的图像。
The gradient — the steepness of the line — gives the velocity.
斜率——也就是线的陡峭程度——给出速度。
A flat line means the object is at rest.
水平线表示物体静止。
A straight slope means a steady velocity.
直的斜线表示速度恒定。
A curve means the velocity is changing.
弯曲的线表示速度在变化。
To find it at one instant, draw a tangent and measure that tangent's gradient.
要求某一瞬间的速度，就画一条切线，量出这条切线的斜率。
Here is a car on a test track.
这里是一辆在测试赛道上的车。
The displacement–time curve starts shallow, then steepens as the car speeds up, then levels off as it settles to a steady speed.
位移–时间曲线开始较缓，随着车加速而变陡， 然后在稳定速度时趋于水平。
At any chosen moment, draw a tangent that just kisses the curve.
在任意选定时刻，画一条刚好贴住曲线的切线。
The gradient of that tangent is the instantaneous velocity right there.
那条切线的斜率就是该处的瞬时速度。
Steeper tangent means faster at that instant.
切线越陡，那一瞬越快。
Flat tangent means momentarily at rest or at peak, depending on the story.
水平切线表示瞬时静止，或处于故事中的峰值，取决于题意。
Next, velocity against time.
接下来是速度对时间的图像。
This graph tells you two things.
这张图告诉你两件事。
Its gradient gives the acceleration.
它的斜率给出加速度。
And the area beneath the line gives the displacement.
而线下方的面积给出位移。
A flat line means constant velocity.
水平线表示速度恒定。
A straight slope means uniform acceleration.
直的斜线表示匀加速。
To get the displacement, find the area — split it into triangles and rectangles.
要求位移，就求面积——把它分成三角形和矩形。
These are the graphical methods the syllabus names, and a large share of the marks in this topic comes from reading or drawing them rather than from any equation.
这些就是考纲点名的图像法， 这个主题里很大一部分分数来自读图或者画图，而不是来自任何公式。
Look at this triangular velocity–time graph.
看这张三角形的速度–时间图。
Velocity rises to a peak, then falls straight back to zero.
速度升到峰值，再直线落回零。
Each straight segment has a constant gradient, so each has uniform acceleration — positive while speeding up, negative while slowing down.
每一段直线斜率恒定， 所以每一段都是匀加速——加速时为正，减速时为负。
The shaded area under the whole triangle is the total displacement for the trip.
整个三角形下方的阴影面积， 就是全程的总位移。
Area of a triangle is one half times base times height.
三角形面积是二分之一乘底乘高。
Count the grid squares if the shape is awkward.
形状别扭时就数格子。
Pair that motion with its acceleration–time graph.
把这段运动和它的加速度–时间图配对。
While the velocity rose at a constant rate, acceleration sat at a constant positive value.
当速度以恒定速率上升时，加速度停在一个恒定的正值。
Then, when the velocity fell at a constant rate, acceleration stepped down to a constant negative value.
然后，当速度以恒定速率下降时，加速度阶梯式降到一个恒定的负值。
A curved velocity–time line would mean changing acceleration.
弯曲的速度–时间线意味着变化的加速度。
Flat on a–t means zero acceleration — constant velocity.
加速度–时间图上水平表示零加速度——匀速。
Read the two graphs together; they tell one story.
两张图一起读；它们讲同一个故事。
Signs matter on a velocity–time graph.
速度–时间图上符号很重要。
Area above the time axis is positive displacement — motion in your chosen positive direction.
时间轴上方的面积是正位移——沿你选定的正方向运动。
Area below the time axis is negative — the object moved backwards.
时间轴下方的面积是负的——物体在后退。
If both appear, subtract the reverse area from the forward area to get the net displacement.
如果两者都有，用前进面积减去后退面积， 就得到净位移。
The total distance is the sum of the absolute areas, with no cancelling.
总路程是各绝对面积之和，不能相互抵消。
For constant acceleration, four equations do all the work.
对于恒定加速度，四个方程就能完成全部工作。
We call them the SUVAT equations, after the five symbols they use: displacement, starting velocity, final velocity, acceleration, and time.
我们称它们为匀加速方程， 取自它们用到的五个符号：位移、初速度、末速度、加速度和时间。
Each equation uses four of the five.
每个方程用到五个中的四个。
The trick is simple: list what you know and what you want, then pick the equation with exactly those symbols.
诀窍很简单：列出你已知的和你想求的， 然后挑出恰好含这些符号的那个方程。
Say them in words so the symbols stick.
用话语说出来，符号就记牢了。
Final velocity equals starting velocity plus acceleration times time.
末速度等于初速度加上加速度乘以时间。
Displacement equals starting velocity times time, plus half acceleration times time squared.
位移等于初速度乘以时间，加上二分之一加速度乘以时间的平方。
Displacement also equals the average of the two velocities, times time.
位移也等于两个速度的平均，再乘以时间。
And final velocity squared equals starting velocity squared plus two times acceleration times displacement.
而末速度的平方等于初速度的平方， 加上二乘加速度乘位移。
Four tools — choose by what is missing.
四件工具——按缺哪个量来选。
Where do they come from?
它们从哪里来？
Straight from the velocity–time graph.
直接来自速度对时间的图像。
The line rises from the starting velocity, at a gradient equal to the acceleration — and that gives the first equation.
这条线从初速度出发上升， 斜率等于加速度——这就给出第一个方程。
The displacement is the area under the line, and that area is a trapezium.
位移是线下方的面积，这块面积是一个梯形。
Its area gives the third equation.
它的面积给出第三个方程。
The other two follow by combining these.
另外两个由这两个组合得到。
You do not memorise them blindly — you can build them.
你不是死记硬背它们——你能推导出来。
Build the remaining links carefully.
仔细把其余环节搭起来。
From the definition of acceleration, a equals final minus starting over time, rearrange to get final equals starting plus a t.
从加速度的定义，加速度等于末减初再除以时间， 整理得到末速度等于初速度加上加速度乘时间。
Put that final velocity into the area formula, and you recover displacement equals u t plus half a t squared.
把这个末速度代入面积公式， 就得到位移等于初速度乘时间加上二分之一加速度乘时间平方。
Removing time from the first two equations leaves final velocity squared equals starting squared plus two a s.
从前两个方程消去时间， 留下末速度平方等于初速度平方加上二乘加速度乘位移。
If a question asks which equation comes from only the gradient of a velocity–time graph, the answer is the first one: final equals starting plus a t.
若题目问哪个方程 只来自速度–时间图的斜率，答案是第一个：末等于初加上加速度乘时间。
On a displacement–time graph for uniform acceleration, the path is a parabola that starts at the origin and steepens.
在匀加速的位移–时间图上，路径是一条从原点出发并逐渐变陡的抛物线。
At any point the slope equals the instantaneous velocity.
任意一点的斜率等于瞬时速度。
Early on the slope is small — the object is still slow.
起初斜率小——物体还慢。
Later the slope is steeper — it has sped up.
后来斜率更陡——它加速了。
That picture is the same story the SUVAT equations tell in algebra.
这幅图与匀加速方程用代数讲的是同一个故事。
Pick a positive direction at the start and keep it.
一开始就选定一个正方向并保持不变。
Anything the other way gets a minus sign.
任何反方向的量都带负号。
For a ball thrown straight up, if up is positive, the starting velocity is positive, but acceleration is minus g, because gravity pulls down.
对于竖直向上抛的球， 若向上为正，初速度为正，但加速度是负的重力加速度，因为重力向下拉。
At the highest point the displacement is still positive, yet the velocity is zero.
在最高点位移仍为正，但速度为零。
Stick to one choice for the whole solution, or the signs will fight you.
整道题坚持同一选择，否则符号会跟你作对。
Let's use one.
我们来用一用。
A car speeds up steadily from eight metres per second to twenty, over a distance of fifty-six metres.
一辆车从每秒八米平稳加速到每秒二十米，经过五十六米的距离。
Find its acceleration.
求它的加速度。
We know the two velocities and the distance, and we want the acceleration — so we choose the equation without time in it.
我们已知两个速度和距离，想求加速度——所以选那个不含时间的方程。
Put the numbers in: twenty squared equals eight squared, plus two times a times fifty-six.
代入数字：二十的平方等于八的平方，加上二乘以加速度乘以五十六。
Solve it, and the acceleration is three metres per second squared.
解出来，加速度是每二次方秒三米。
Free fall is just constant acceleration, downward, from gravity.
自由落体只是恒定的、向下的加速度，来自重力。
Near the ground it is about nine point eight metres per second squared, the same for every mass.
在地面附近它约为每二次方秒九点八米， 对每个质量都一样。
Throw a ball straight up, and the motion is symmetric: it slows, stops for an instant at the top, then falls back the same way.
把球竖直向上抛，运动是对称的：它减速，在最高点停顿一瞬， 然后沿同样的路径落回。
At the top, set the velocity to zero.
在最高点，把速度设为零。
A ball thrown up at twenty metres per second reaches about twenty metres high.
以每秒二十米向上抛的球， 能上升到约二十米高。
With air resistance the picture changes: the resultant force is smaller than the weight, so the acceleration is less than g, and because the resistance grows with speed the acceleration keeps decreasing until it reaches zero at the terminal velocity.
有空气阻力时情况就变了： 合力小于重力，所以加速度小于 g， 而且因为阻力随速度增大，加速度不断减小， 直到在收尾速度处变为零。
When air resistance can be ignored, drop from rest is the simplest free-fall case.
当可以忽略空气阻力时，从静止释放是最简单的自由落体情形。
Height equals half g times time squared.
高度等于二分之一重力加速度乘以时间的平方。
Speed equals g times time.
速率等于重力加速度乘以时间。
And speed squared equals two g times height.
而速率的平方等于二乘重力加速度乘高度。
These three are just SUVAT with starting velocity zero and acceleration equal to g downward.
这三条只是初速度为零、加速度为向下重力 时的匀加速方程。
Use them for a ball released from rest above the ground.
用于从地面上方静止释放的球。
For a ball thrown straight up with speed u, greatest height is u squared over two g.
对于以速率 u 竖直上抛的球，最大高度是 u 的平方除以二 g。
Time to the top is u over g — put final velocity zero in final equals starting minus g t.
到顶时间是 u 除以 g—— 在末速度等于初速度减 g 乘时间中把末速度设为零。
Total time to fall back to the start height is twice that, two u over g, because the motion is symmetric.
落回起始高度的总时间是它的两倍， 二 u 除以 g，因为运动是对称的。
Same path up, same path down, same times.
上去同路径，下来同路径，时间也相同。
Work the numbers carefully.
仔细算数字。
A ball is thrown straight up at twenty metres per second.
球以每秒二十米竖直上抛。
Take g as nine point eight one.
取重力加速度为九点八一。
At the highest point final velocity is zero, so height is u squared over two g: four hundred divided by two times nine point eight one, which is four hundred over nineteen point six two — about twenty point four metres.
在最高点末速度为零， 所以高度是 u 的平方除以二 g：四百除以二乘九点八一，也就是四百除以十九点六二—— 约二十点四米。
That is the handout value; the rough twenty metres was a quick check.
那是讲义上的值；粗略的二十米只是快速验算。
How do we measure gravity in the lab?
我们如何在实验室里测量重力？
Drop a ball, and measure the height it falls and the time it takes.
让一个球下落，测量它下落的高度和所用的时间。
An electromagnet releases the ball and starts a timer; a trapdoor stops it — so no slow human reaction time creeps in.
一个电磁铁释放球并启动计时器；一个活门让计时停止——这样就没有缓慢的人类反应时间混进来。
Repeat for several heights, then plot the height against the time squared.
对几个不同的高度重复，然后画出高度对时间平方的图。
The line comes out straight, and its gradient is half of gravity.
这条线是直的，它的斜率是重力的一半。
Study the apparatus.
仔细看装置。
A release switch cuts the current to the electromagnet so the steel ball drops and the electronic timer starts.
释放开关切断电磁铁电流，钢球落下，电子计时器启动。
The ball falls a measured height h and hits a trapdoor switch that stops the timer.
球下落测量高度 h， 撞到活门开关使计时停止。
From height equals half g t squared you rearrange: g equals two h over t squared.
由高度等于二分之一 g 乘时间平方整理：g 等于二 h 除以时间平方。
Light gates can replace the trapdoor — same idea, no human reaction time.
光电门可以代替活门——同一思路，没有人类反应时间。
Good technique cuts error.
好方法能减小误差。
Repeating for several heights and drawing the best straight line reduces random error — scatter averages out.
对几个高度重复并画最佳直线，可减小随机误差——离散会平均掉。
An electronic timer, light gates, or a switch the ball hits removes reaction-time error that a hand-held stopwatch would add.
电子计时器、光电门，或球撞击的开关，能去掉手持秒表带来的反应时间误差。
Read the gradient of h against t squared carefully: it is half of g, so g is twice the gradient.
仔细读 h 对时间平方的斜率：它是 g 的一半，所以 g 是斜率的两倍。
Quote both the value and how you found it.
既要报出数值，也要说明你如何得到它。
Now, motion in two directions at once.
现在看同时在两个方向上的运动。
Watch two balls: one simply dropped, the other thrown sideways.
看这两个球：一个只是被放下，另一个被水平抛出。
They fall at exactly the same rate, and they land at the same moment.
它们以完全相同的速率下落，并在同一时刻着地。
The sideways motion does not change the falling at all.
水平方向的运动丝毫不改变下落。
Horizontal and vertical motion are independent — so we can treat each one on its own.
水平运动和竖直运动是相互独立的——所以我们可以分别处理每一个方向。
Water jets from a sprinkler make the same idea visible outdoors.
喷灌器喷出的水柱，让同样的道理在户外可见。
Streams leave one nozzle at the same speed but different angles — thirty, forty-five, sixty degrees.
水流以相同速率、不同角度离开同一喷嘴—— 三十度、四十五度、六十度。
Each traces a parabola.
每一道都画出抛物线。
The forty-five degree jet reaches the greatest range on level ground.
在平地上四十五度的水柱射程最远。
Treat each jet as a projectile: constant horizontal speed, constant vertical acceleration g.
把每一道水柱当作抛体：水平匀速，竖直恒定加速度 g。
Take a ball thrown horizontally off a cliff.
拿一个从悬崖水平抛出的球。
Split it into two problems.
把它分成两个问题。
Going down, it starts from rest and speeds up under gravity — so the fall time depends only on the height.
竖直方向上，它从静止开始， 在重力作用下加速——所以下落时间只取决于高度。
Going across, it keeps a steady speed the whole way.
水平方向上，它全程保持匀速。
From a twenty-metre cliff, thrown at fifteen metres per second, the fall takes about two seconds, and it lands about thirty metres out.
从二十米高的悬崖，以每秒十五米抛出，下落约需两秒，落点在约三十米之外。
Comparing two objects is the classic version.
比较两个物体是这类题的经典版本。
If A is dropped and B is thrown horizontally from the same height at the same moment, both reach the ground at the same time, because their vertical motions are identical.
如果 A 被松手落下，B 在同一时刻从同样的高度水平抛出， 两者会同时落地，因为它们的竖直运动完全一样。
If B is instead thrown with an upward component it takes longer, because it must first rise and come back down to the height it started from.
如果 B 改成带有向上分量地抛出，它用的时间更长， 因为它必须先上升，再回到出发的高度。
Write the two lines cleanly.
把两行干净地写出来。
Horizontal: constant velocity u H, so range x equals u H times t.
水平：恒定速度 u 水平，所以射程 x 等于 u 水平乘 t。
Vertical: starts from rest, so height h equals half g t squared, and vertical speed is g t.
竖直：从静止开始，所以高度 h 等于二分之一 g 乘 t 的平方，竖直速率是 g 乘 t。
Solve the vertical equation for t first — time depends only on height, not on the throw speed.
先从竖直方程解出 t——时间只取决于高度，与抛出速率无关。
Then multiply by u H for the range.
再乘以 u 水平得射程。
The horizontal velocity graph is a flat line; the vertical velocity graph is a straight line from the origin with gradient g.
水平速度图是一条水平线；竖直速度图是从原点出发、斜率为 g 的直线。
Launch at an angle, and the very same idea works.
以一定角度发射，同样的道理依然成立。
Split the starting velocity into two parts.
把初速度分成两部分。
The horizontal part is the speed times the cosine of the angle.
水平部分是速率乘以角度的余弦。
The vertical part is the speed times the sine of the angle.
竖直部分是速率乘以角度的正弦。
The horizontal part stays constant.
水平部分保持恒定。
The vertical part shrinks, stops at the top, then grows downward.
竖直部分减小，在最高点停下，然后向下增大。
The path traced out is a perfect parabola.
画出的路径是一条完美的抛物线。
Examiners often ask you to sketch the two velocity components against time on the same axes, taking upwards as positive.
考官经常要你在同一坐标轴上画出两个速度分量随时间的变化，取向上为正。
The horizontal component is a flat line at u cos theta for the whole flight.
水平分量在整个飞行过程中是一条高度为 u cos θ 的水平直线。
The vertical component is a straight line of gradient minus g, starting at u sin theta, crossing zero at the top of the flight and going negative on the way down.
竖直分量是一条斜率为负 g 的直线，从 u sin θ 出发， 在最高点穿过零，下降段变为负值。
The diagram shows the launch: initial speed u at angle theta above the horizontal, resolved into horizontal component u cosine theta and vertical component u sine theta.
图上显示发射：初速率 u 以水平面以上角度 theta 射出，分解为水平分量 u 余弦 theta 和竖直分量 u 正弦 theta。
Those two components never mix — treat the horizontal, at constant velocity, and the vertical, with a equal to g, separately.
这两个分量永不混合。
Horizontal motion is constant velocity.
水平运动是匀速。
Vertical motion is free fall with a non-zero starting speed upward.
竖直运动是带非零向上初速的自由落体。
The shared clock t links the two SUVAT problems.
共同的时钟 t 把两个匀加速问题连在一起。
From level ground back to level ground, the range R is the horizontal distance from launch to landing.
从平地回到平地，射程 R 是从发射到落地的水平距离。
Maximum height H sits at the midpoint of a symmetric flight.
最大高度 H 位于对称飞行的中点。
At the highest point, vertical velocity is zero, but horizontal velocity is still u cosine theta.
在最高点，竖直速度为零，但水平速度仍是 u 余弦 theta。
Time to the top is u sine theta over g.
到顶时间是 u 正弦 theta 除以 g。
Total flight time is twice that.
总飞行时间是它的两倍。
Use those to find H and R without guessing.
用这些求 H 和 R，不必猜测。
When a ball bounces, its velocity–time graph is a set of straight sloping lines — constant g between impacts — with a sudden jump at each bounce.
当球弹跳时，它的速度–时间图是一组直线斜线段——撞击之间是恒定的 g—— 每次弹跳有一个突然的跳跃。
The velocity flips direction, and if some energy is lost, the rebound speed is smaller than the impact speed.
速度方向翻转，若有能量损失，反弹速率小于撞击速率。
Add up the times of the segments for total flight time.
把各段时间加起来得到总飞行时间。
Add the distances of the up and down legs carefully, watching signs, for net displacement.
仔细把上下各段距离相加，注意符号，求净位移。
When two objects move along the same line, write a displacement equation for each.
当两个物体沿同一直线运动时，为每一个写一个位移方程。
Use the same start time and the same positive direction.
使用相同的起始时间和 相同的正方向。
They are level again where the two displacement–time graphs cross — same s at the same t.
它们再次并排之处，就是两张位移–时间图相交之处——同一时刻同一位移。
That crossing is the meeting event the question asks for.
那个交点就是题目所问的相遇事件。
Concrete case.
具体情形。
A goods train at constant velocity u G, and an express train starting from rest with acceleration a, both pass the same point at time zero.
一列匀速 u 货 的货车，和一列从静止以加速度 a 起步的快车， 都在时刻零经过同一点。
Goods displacement is u G times t.
货车位移是 u 货乘 t。
Express displacement is half a t squared.
快车位移是二分之一 a 乘 t 的平方。
Set the two displacements equal for the next time they are level: u G t equals half a t squared.
令两位移相等，求下次并排：u 货 t 等于二分之一 a t 平方。
Cancel one t, and the meeting time is two times u G over a.
约去一个 t， 相遇时间是二倍 u 货除以 a。
Five habits for every kinematics problem.
每道运动学题的五个习惯。
Draw a diagram and mark the positive direction.
画图并标出正方向。
List the SUVAT symbols with known and unknown values, including signs.
列出匀加速符号及其已知未知值，含符号。
Choose the SUVAT equation with exactly the four you have plus the one you want.
选恰好含你已有的四个加上想求的那一个的方程。
For projectiles, split into horizontal and vertical problems, linked only by the shared time.
对抛体，分成水平和竖直问题， 只由共同时间相连。
Always check the units of your answer, and that its size is sensible.
永远检查答案的单位，以及数量级是否合理。
Three ways to keep your marks.
三个保住分数的方法。
First, use the SUVAT equations only when the acceleration is constant.
第一，只有在加速度恒定时才用匀加速方程。
Second, choose a positive direction and stick to it — usually gravity is negative.
第二，选定一个正方向并始终保持——通常重力取负。
Third, for any projectile, split the motion into horizontal and vertical, joined only by the shared time.
第三，对任何抛体， 把运动分成水平和竖直两部分，只由共同的时间联系起来。
Get these right, and motion problems fall into place.
把这些做对，运动问题就迎刃而解。
The fixed-wording definitions, one answer only.
固定措辞的定义，只给一个答案。
Distance: the total length of the path travelled, a scalar.
路程：所走路径的总长度，是标量。
Displacement: the distance moved in a stated direction from start to finish, a vector.
位移：从起点到终点、沿指定方向移动的距离，是矢量。
Speed: the rate of change of distance with time.
速率：路程对时间的变化率。
Velocity: the rate of change of displacement with time.
速度：位移对时间的变化率。
Acceleration: the rate of change of velocity with time.
加速度：速度对时间的变化率。
Uniform acceleration: acceleration constant in magnitude and direction.
匀加速：大小和方向都恒定的加速度。
Acceleration of free fall: the acceleration of an object falling freely under gravity alone, with air resistance negligible.
自由落体加速度：物体只在重力作用下自由下落时的加速度，空气阻力可忽略。
And the traps.
再说陷阱。
With air resistance ignored the heavier ball does not land first or faster — both fall with the same acceleration and land at the same speed.
忽略空气阻力时，重的球并不会先落地，也不会落得更快—— 两者加速度相同，落地速度也相同。
On a velocity-time graph the gradient is acceleration and the area is displacement; take the one the question asks for.
在速度—时间图上，斜率是加速度，面积是位移；题目问哪个就取哪个。
Constant acceleration is a straight line, not a curve.
匀加速对应直线，不是曲线。
Once you call up positive, a is minus nine point eight one for the whole flight, on the way down too.
一旦你把向上定为正，整个飞行过程中 a 都是负九点八一，下落段也是。
And when the acceleration is changing — air resistance, a curved graph — no SUVAT equation applies; only the graph methods work.
另外，加速度在变化时——有空气阻力、图线弯曲——任何 SUVAT 公式都不适用， 只有图像法有效。
One last graph reminder before you leave.
离开前最后一条图像提醒。
On a velocity–time graph, gradient equals acceleration and area equals displacement.
在速度–时间图上，斜率等于加速度，面积等于位移。
Split awkward shapes into triangles and rectangles.
把别扭的形状拆成三角形和矩形。
Area of a triangle is half base times height; area of a rectangle is base times height.
三角形面积是二分之一底乘高；矩形面积是底乘高。
Write the method in words as you compute — examiners award method marks even if arithmetic slips.
计算时用文字写出方法——即使算术出错，考官仍给方法分。