平均速度公式

了解旅行发生的速度需要了解平均速度。旅行的速度可能会不时改变。在这种情况下，确定平均速度对于估计完成航程的速度至关重要。

平均速度

平均速度公式用于计算均匀速率，即任何物体以恒定且可预测的速率移动的速率。平均速度是一个标量。它没有方向，由大小表示。让我们看看如何计算平均速度，计算平均速度的公式，以及平均速度的一些解决案例。

It is the total distance covered divided by the total time taken to cover that distance.

平均速度公式

Average Speed = Total distance covered / Total Time taken

推导

Let’s imagine a man journeys to his favorite hilly place at different speeds, v₁, v₂, v₃, …., and so on, over time intervals of t₁, t₂, t₃ ,…, and so on. As a result, the total distance travelled is: v₁t₁ + v₂t₂ + v₃t₃ + …. v_nt_n. The total time taken is t₁ + t₂ + t₃ + ….. + t_n. 

As a result, the average speed at which he completed his voyage is,

V_avg = (v₁t₁ + v₂t₂ + v₃t₃ + . . . . + v_nt_n) / (t₁ + t₂ + t₃ +. . .+ t_n)

If assumed that the time spent in each period is the same, t₁ = t₂ = t₃ = . . . . = t_n, the following new equation is obtained:

V_avg = (v₁ + v₂ + v₃ +. . . +v_n) / n

The average speed is the arithmetic mean of the individual speeds, as can be seen.

示例：汽车旅行需要 3 个小时。第一小时行驶 38 英里，第二小时行驶 54 英里，第三小时行驶 55 英里。

解决方案：

Speed in first hour = 38 miles/hour

Speed in second hour = 54 miles/hour

Speed in third hour = 55 miles/hour

During the three-hour ride, travel at three distinct speeds.

If one wishes to calculate the average speed for a three-hour journey, then, take the ratio of Total distance covered and total time taken. Therefore,

Total distance covered = (Speed in a first hour + Speed in second-hour + Speed in the third hour)

∴ Total distance covered = (38 + 54 + 55) = 142 miles ⇢ (Equation 1)

Total time is taken = 3 hours ⇢ (Equation 2)

Therefore, the formula of average speed,

Average Speed = Total distance covered / Total Time taken

∴ Average Speed = 147 / 3 ⇢ (from equation 1 and 2)

∴ Average Speed = 49 miles/hour

平均速度单位

如果计算平均速度，在这种情况下为单位，你会看到它如下：

= (2(m/s)(m/s)) / ((m/s) + (m/s))

去掉常用词，回到单位m/s。

以不同的方式，

如果有人以一定的速度从 A 点行进到 B 点，比如说每小时 m 英里。该人以不同的速度从 B 点前往 A 点，例如每小时 n 米。因此，该人在两个方向上通过的距离相同，但速度不同。那么如何求平均速度呢？

使用公式，平均速度 = (2mn) / (m + n)

推导

Let’s say a particle travels variable distances s₁, s₂, s₃, s₄ …., s_n in the same direction with varying velocities v₁, v₂, v₃ …., v_n. The time is equal to the division of distance by the time, so we get the following formula for this scenario,

Total time taken ‘t’ = (s₁ / v₁) + (s₂ / v₂) + (s₃ / v₃) + … + (s_n / v_n)

Here, Speed = Distance / Time, so the formula of average speed is,

V_avg = (s₁ + s₂ + ….) / ((s₁ / v₁) + (s₂ / v₂ ) +….)

If assume that the variable distances are equal, s₁ = s₂, the formula becomes:

= 2s / ((s / v₁) + (s / v₂) + …)

= 2v₁v₂ / ((1 / v₁) + (1 / v₂))

∴ V_avg = 2v₁v₂ / (v₁ + v₂)

The idea that average speed is the harmonic mean of particular speeds is vividly expressed in this statement.

示例：Rohit 以设定的速度从 A 点行进到 B 点。当他从 B 地返回到 A 地时，他以每小时 56 米的速度行进。如果他整个旅程的平均速度是每小时 99 米，求他从 A 点到 B 点的速度。

解决方案：

考虑一下，“a”是从 A 地到 B 地的速度。

从 A 地到 B 地的速度 = 56 米/小时

他在两个方向上覆盖相同的距离。

平均速度公式，

平均速度 = (2mn) / (m + n)

这里，m = 从 A 地到 B 地的速度，n = 从 A 地到 B 地的速度 = 56 米/小时

∴ 99 = (2 × m × 56) / (m + 56)

∴ 99(m + 56) = 112m

∴ 99m + 5544 = 112m

∴ 5544 = 112m – 99m

∴ 5544 = 13m

∴ m = 426.46 米/小时

距离

Distance is defined as the total length of a path connecting two places.

距离的公式是，

距离 = 速率 × 时间

平均速度的真实示例

• Swapnil 是一位好友，他在九个月的时间里刚刚完成了三本书。他是怎么做到的？

通过使用简单的技术。他每天写1000字。 （这大约需要 2 到 3 页）他连续 253 天每天都这样做。考虑一下这种方法，与作家躲在小屋里数周，像疯子一样写作来完成他们的小说的传统想法相比。机舱疯子有很高的“最大速度”——每天可能有 20 或 30 页。然而，以如此不可持续的速度几周后，这本书或作者都将完成。另一方面，Swapnil 的最高速度从未接近机舱疯狂作家的最高速度。不过，他的平均速度在一两年内显着提高。

• 任何人都可以激发灵感，去健身房，为一次锻炼而努力。这就是最高速度。我们花了很多时间担心它。你锻炼的强度是多少？是什么激励你？你有多努力地逼迫自己？

但是，如果对上个月的所有天数进行平均呢？其中有多少天涉及某种体育活动？过去三个月发生了什么？还是前一年？你的平均速度是多少？

如果这样看，人们可能会注意到他们生病了一周，他们在漫长的一天工作后跳过了健身房几次，而且他们也在路上待了两周。突然间，人们会意识到，虽然有时最高速度可能非常快，但平均速度却远低于人们的想象。

概括

Average Speed is defined as the total distance covered divided by the total time taken to cover that distance.

Formula of Average Speed:

Average Speed = Total distance covered / Total Time taken

If someone travels from point A to point B at a certain speed, say m miles per hour. He travels from point B to point A at a different rate, say n meter per hour. He crosses the same distance in both directions, but at different speeds.

Formula of Average Speed:

Average Speed = (2mn) / (m + n)

示例问题

问题 1：Dhanraj 以每小时 50 英里的速度行驶 3 小时，以每小时 60 英里的速度行驶 4 小时，以每小时 80 英里的速度行驶 5 小时。他在整个旅程中的平均行驶速度是多少？

回答：

The total distance traveled in the first three hours is = Rate × Time 

Distance = 50 × 3

∴ Distance = 150 miles

The total distance traveled in the next four hours is = Rate × Time

Distance = 60 × 4

∴ Distance = 240 miles 

The total distance traveled in the last five hours is = Rate × Time

Distance = 80 × 5

∴ Distance = 400 miles

Then, Total distance covered = 150 + 240 + 400

∴ Total distance covered = 790 miles

Then, Total Time taken = 3 + 4 + 5

∴ Total Time taken = 12 hours

Here,

Average Speed = Total distance covered / Total Time taken

∴ Average Speed = 790 / 12

∴ Average Speed = 65.8333

As a result, the overall average speed is 65.8333 miles per hour.

问题2：定义平均速度及其公式。

回答：

Average speed is defined as the total distance covered divided by the total time taken to cover that distance.

Formula of Average Speed:

Average Speed = Total distance covered / Total Time taken

问题 3：以每小时 40 英里的速度，从 A 点行驶到 B 点需要 5 个小时。他从 B 地返回到 A 地，速度提高了 25%。计算整个旅程的平均速度。

回答：

Speed from place A to place B = 40 miles per hour.

Speed from place B to place A = 50 miles per miles. (25% increased)

Average Speed = (2mn) / (m +n)

Here, m = 40, n = 50

Average Speed = (2 × 40 × 50) / (40 + 50)

∴ Average Speed = 44.44 

As a result, the overall average speed is 44.44 miles per hour.

问题 4：平均速度、总行驶距离、总用时之间的关系。

回答：

Here,

Average Speed = Total distance covered / Total Time taken

Average speed directly proportional to Total distance covered and inversely proportional to Total time taken.

问题 5：平均速度是矢量还是标量？

回答：

Average speed is a scalar quantity.

问题6：平均速度公式究竟表明了什么？

答案：

The average speed formula, often known as v_avg, is used to calculate the average speed of a body that varies continuously over time intervals. If we have the final velocity, v, and the initial velocity, u, we can calculate v_avg using the formula.