Motion Graphs

运动图线

Constant acceleration motion can be characterized by motion equations and by motion graphs. The graphs of distance, velocity and acceleration as functions of time below were calculated for one-dimensional motion using the motion equations in a spreadsheet. The acceleration does change, but it is constant within a given time segment so that the constant acceleration equations can be used. For variable acceleration (i.e., continuously changing), then calculus methods must be used to calculate the motion graphs.

匀加速运动可以通过运动方程和运动图象来描述。下面的图象是在使用运动方程的电子表格中计算出的，展示了距离、速度和加速度作为时间函数的图象。加速度会发生变化，但在给定的时间段内是恒定的，因此可以使用恒定加速度方程。对于变化的加速度（即连续变化），则必须使用微积分方法来计算运动图象。

A considerable amount of information about the motion can be obtained by examining the slope of the various graphs. The slope of the graph of position as a function of time is equal to the velocity at that time, and the slope of the graph of velocity as a function of time is equal to the acceleration.

通过分析各种图的斜率，可以获得关于运动的大量信息。位置作为时间函数的图的斜率等于该时刻的速度，而速度作为时间函数的图的斜率等于加速度。

The Slopes of Motion Graphs

运动图的斜率

A considerable amount of information about the motion can be obtained by examining the slope of the various motion graphs. The slope of the graph of position as a function of time is equal to the velocity at that time, and the slope of the graph of velocity as a function of time is equal to the acceleration.

通过检查各种运动图象的斜率，可以获得关于运动的大量信息。位置作为时间函数的图象的斜率等于该时刻的速度，而速度作为时间函数的图象的斜率等于加速度。

In this example where the initial position and velocity were zero, the height of the position curve is a measure of the area under the velocity curve. The height of the position curve will increase so long as the velocity is constant. As the velocity becomes negative, the position curve drops as the net positive area under the velocity curve decreases. Likewise the height of the velocity curve is a measure of the area under the acceleration curve. The fact that the final velocity is zero is an indication that the positive and negative contributions were equal.

在这个初始位置和速度均为零的例子中，位置曲线的高度是速度曲线下的面积的度量。只要速度保持恒定，位置曲线的高度就会持续增加。当速度变为负值时，位置曲线会下降，因为速度曲线下的净正面积会减少。同样，速度曲线的高度是加速度曲线下的面积的度量。最终速度为零的事实表明正负贡献相等。