●

They feel stationary relative to the train.
乘客感觉自己相对于火车是静止的。

●

They see the platform and the person moving backward.
乘客看到站台和站台上的人正在向后运动。

●

They see the train moving forward.
他们看到火车在向前移动。

●

They see the passenger inside the train moving forward along with the train.
他们看到火车里的乘客与火车一同向前运动。

1.

Scalar Quantities :
标量：

●

Only have magnitude.
只表示大小

●

Mathematical operations are simple :
数学运算很简单：

●

Addition: Just add numbers.
相加：数字相加既可。

●

Multiplication: Just multiply numbers.
相乘：只是数字相乘。

●

how to determine positive or negative.
如何确定是正或负。

●

The sign of a scalar quantity depends on how it's being measured. For example: a temperature of -5°C means it's 5 degrees below freezing.
标量的正负号取决于衡量方式。例如：温度-5°C表示其温度比零度低五度。

2.

Vector Quantities :
矢量：

●

Have both magnitude and direction.
表示大小和方向。

●

Mathematical operations are more complex:
数学运算更加复杂：

●

Addition: Must consider direction (parallelogram method).
相加：必须要考虑方向 （平行四边形法则）。

●

Multiplication: Need a complex method, you don't need to know that as a pilot.
相乘：需要用很复杂的计算方式，作为飞行员用不到这个。

●

Can be broken into components (x, y, z).
可被分解成沿x，y，z轴的分量。

●

how to determine positive or negative.
如何确定是正或负。

●

The sign (positive/negative) of vector depends on its direction relative to a reference frame.
矢量的正负取决于其相对于参考系的方向。

Choose a reference direction as positive (like right or up).
选定一个方向为正（比如上或右）。

Vector pointing in that direction are positive.
指向选定方向的矢量为正。

Vector pointing in the opposite direction are negative.
指向反向的为负。

1.

Composition of Vectors :
矢量的合成：

●

Place vectors A and B tail to tail at origin.
在原点上将矢量A和B尾部相连。

●

Draw parallel lines to form parallelogram.
画平行线来做出平行四边形。

●

Diagonal gives resultant vector (C).
对角线便是得出的矢量(C)。

●

$\mathrm{Vector\; (C)}=\frac{\mathrm{Vector\; (B)}}{\mathrm{cos\theta }}=\frac{\mathrm{Vector\; (A)}}{\mathrm{sin\theta }}$

2.

Decomposition of Vectors :
矢量的分解：

●

It is the same as the method of compositing vectors, just used in the reverse way.
它与合成矢量的方法是一样的，只是反过来用。

●

$\mathrm{Vector\; (A)}=\mathrm{Vector\; (C)}\times \; <!--\; multiplication\; sign\; -->\mathrm{sin\theta }$

●

$\mathrm{Vector\; (B)}=\mathrm{Vector\; (C)}\times \; <!--\; multiplication\; sign\; -->\mathrm{cos\theta }$

1.

Distance :
距离：

Distance is the total length of the actual path traveled, regardless of direction. It's always positive and is what you'd measure if you tracked the exact route taken - like your car's odometer or a GPS tracking your run. For example, if you walk 3 kilometers east, then 4 kilometers north, then 3 kilometers west, your total distance is 10 kilometers.
距离是实际经过的总距离，无关方向。距离永远为正，是精确测量走过的每一段路程所得出的长度 - 就像你汽车上的里程表，或是GPS跑步测距。 举个例子，如果你向东走3公里，再向北走4公里，再向西走3公里。总距离为10公里。

2.

Displacement :
位移：

Displacement is the straight-line difference between your starting and ending positions - basically "as the crow flies." It includes both magnitude and direction. Using the same example: after walking east, north, and west, you'd end up just 4 kilometers north of where you started. That 4 kilometers north is your displacement.
位移是起点和终点的直线距离 - 可以说是“最短捷径”。其表示大小和方向。用同一个例子：在向东，向北，向西行走后，你离起点只有向北4公里的距离。向北4公里就是你的位移。