Velocity–time graphs | 速度-时间图像

📚 Velocity–time graphs | 速度-时间图像

A velocity-time graph is one of the most important tools in A-level mechanics. It shows how an object's velocity changes with time, and it allows you to calculate acceleration from the gradient and displacement from the area under the graph. Mastering these graphs is essential for Edexcel exam questions on kinematics.

速度-时间图像是 A-level 力学中最重要的工具之一。它显示物体速度随时间的变化情况，让你可以从斜率求加速度，并从图像下方面积求位移。掌握这类图像对 Edexcel 运动学考题至关重要。

1. What a velocity-time graph shows | 速度-时间图像表示什么

On a velocity-time graph, time t is plotted on the horizontal axis and velocity v is plotted on the vertical axis. The graph can be above or below the time axis, showing the direction of motion compared with a chosen positive direction.

在速度-时间图像中，时间 t 标在横轴，速度 v 标在纵轴。图像可以位于时间轴上方或下方，表示与选定正方向相比的运动方向。

If the line lies above the t-axis, the velocity is positive; if it lies below, the velocity is negative. A negative velocity does not automatically mean slowing down unless the acceleration is in the opposite direction to the velocity.

如果图像位于 t 轴上方，速度为正；位于下方则速度为负。负速度不一定表示减速，除非加速度方向与速度方向相反。

The graph is a visual record of the whole motion in one diagram. You can see when the object speeds up, slows down, stops, or reverses direction.

图像是在一个图中完整记录运动的可视化信息。你可以看到物体何时加速、减速、停止或改变运动方向。

---

2. Reading velocity and direction | 读取速度与方向

y time. For example, at t = 4 s the graph may give v = 12 m s⁻¹ in the positive direction.

你可以通过读取任意时刻的纵坐标得到瞬时速度。例如，在 t = 4 s 时图像可能给出 v = 12 m s⁻¹ 的正方向速度。

t t = 0. The final velocity is the value at the end of the time interval being considered.

初速度 u 是图像在 t = 0 处与纵轴相交的值。末速度是所考虑时间区间结束时的速度值。

When the graph crosses the time axis, the velocity is zero at that instant. If the graph then continues on the opposite side of the axis, the object has changed direction.

当图像穿过时间轴时，该时刻速度为零。如果图像随后继续到时间轴的另一侧，物体就改变了运动方向。

---

3. Gradient equals acceleration | 斜率等于加速度

The gradient of a velocity-time graph is the rate of change of velocity with time, so it equals acceleration. For a straight-line segment, the acceleration is constant and is given by the formula below.

速度-时间图像的斜率是速度随时间的变化率，因此等于加速度。对于直线段，加速度恒定，由以下公式给出。

a = Δv ÷ Δt

Units of acceleration are m s⁻². A positive gradient means acceleration in the positive direction, while a negative gradient means acceleration in the negative direction.

加速度的单位是 m s⁻²。斜率为正表示正方向的加速度，斜率为负表示负方向的加速度。

If the graph is curved, the gradient at a point can be found by drawing a tangent to the curve. The slope of that tangent is the instantaneous acceleration at that time.

如果图像是曲线，可以通过画切线求某一点的斜率。该切线的斜率就是该时刻的瞬时加速度。

---

4. Area equals displacement | 面积等于位移

The area between a velocity-time graph and the time axis gives displacement. Areas above the axis are positive displacement, and areas below the axis are negative displacement.

速度-时间图像与时间轴之间的面积表示位移。轴上方的面积为正位移，轴下方的面积为负位移。

To find total displacement, add all areas using their signs. To find total distance travelled, add the absolute values of all areas, ignoring whether they are above or below the axis.

求总位移时，要按正负号相加所有面积。求总路程时，则将所有面积的绝对值相加，不论其位于轴上方还是下方。

Common shapes are rectangles, triangles and trapeziums. Use the appropriate area formula for each section of the graph.

常见图形包括矩形、三角形和梯形。对图像的每一段使用相应的面积公式即可。

---

广告 / Sponsored

5. Uniform acceleration segments | 匀加速段

A straight, sloping line on a velocity-time graph indicates uniform acceleration. The velocity changes by equal amounts in equal time intervals.

速度-时间图像上一条倾斜直线表示匀加速运动。速度在相等时间间隔内变化相等的量。

For a segment starting with initial velocity u and ending with final velocity v over time t, the acceleration and displacement can be found using the following equations.

对于初速度为 u、末速度为 v、时间为 t 的一段，加速度和位移可用以下公式求出。

a = (v − u) ÷ t

s = ½(u + v)t

triangle with area ½vt. If it comes to rest, v = 0, and the same triangle formula applies.

如果物体从静止出发，u = 0，因此面积是三角形，面积为 ½vt。如果物体减速到静止，v = 0，同样适用三角形公式。

---

6. Constant velocity and rest | 匀速与静止

leration is zero. The displacement during this time is the area of a rectangle: s = v × t.

速度-时间图像上的水平线表示速度恒定，因此加速度为零。这段时间内的位移是矩形面积：s = v × t。

0 and the object is at rest. No area is added to displacement, but time continues to pass.

如果水平线位于时间轴上，则 v = 0，物体处于静止状态。位移不增加，但时间继续流逝。

unless v = 0. A horizontal line at v = 10 m s⁻¹ still represents motion at constant speed.

考试中不要认为水平线就表示物体已停止，除非 v = 0。v = 10 m s⁻¹ 处的水平线仍表示物体在匀速运动。

---

7. Motion with changing acceleration | 变加速运动

When a velocity-time graph is a curve, the acceleration is not constant. The gradient changes from point to point, so you must use a tangent to estimate the acceleration at a specific time.

当速度-时间图像为曲线时，加速度不是恒定的。斜率逐点变化，因此必须用切线来估算某一特定时刻的加速度。

The area under a curved graph can still be used to find displacement. In Edexcel exam questions, you may count squares or use a given approximation such as the trapezium rule if necessary.

曲线下的面积仍可用于求位移。在 Edexcel 考题

Published by TutorHao | A-Level Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）