# Average Speed and Average Power confusion

• LLT71
In summary, the conversation discussed the concept of taking averages and how it applies to average speed and average signal power. It was also mentioned that integrals can be used to calculate time-weighted and mass-weighted averages.
LLT71
I found it somehow tricky to understand average speed and average power in mathematical fashion.
I suppose general idea of taking average of some quantity is: sum of all values/number of values.
how that idea fit's into idea of average speed=distance traveled/time traveled

similarly, average signal power:

why is it over T?

LLT71 said:
I found it somehow tricky to understand average speed and average power in mathematical fashion.
I suppose general idea of taking average of some quantity is: sum of all values/number of values.
how that idea fit's into idea of average speed=distance traveled/time traveled

similarly, average signal power:

why is it over T?

Do you understand integrals in discrete terms?

https://betterexplained.com/articles/a-calculus-analogy-integrals-as-multiplication/

LLT71
time-weighted average of Q(t)=##\displaystyle\frac{\int_0^T Q(t)\ dt}{ \int_0^T \ dt }=\frac{\int_0^T Q(t)\ dt}{ T } ##
(For example, the average-velocity is a time-weighted average of velocity:
##\displaystyle\frac{\int_{t_1}^{t_2} v(t) \ dt}{ \int_{t_1}^{t_2} \ dt }=\frac{\int_{t_1}^{t_2} \frac{dx(t)}{dt} \ dt}{ \int_{t_1}^{t_2} \ dt }=\frac{x(t_2)-x(t_1)}{ t_2-t_1}=\frac{\Delta x}{ \Delta t} ##.

the average-speed is a time-weighted average of speed:
##\displaystyle\frac{\int_{t_1}^{t_2} |v(t)| \ dt}{ \int_{t_1}^{t_2} \ dt }=\frac{\int_{t_1}^{t_2} |\frac{dx(t)}{dt}| \ dt}{ \int_{t_1}^{t_2} \ dt }=\frac{d}{ t_2-t_1}=\frac{d}{ \Delta t} ##.
)z-weighted average of Q(z)=##\displaystyle\frac{\int_0^Z Q(z)\ dz}{ \int_0^Z \ dz }=\frac{\int_0^Z Q(z)\ dz}{ Z }##
(For example, the center of mass is a mass-weighted average of position:
##\displaystyle\frac{m_1x_1+m_2x_2+m_3x_3 }{m_1+m_2+m_3}=\frac{m_1x_1+m_2x_2+m_3x_3 }{M}##.
If all of the "masses" are equal (so each item has equal "weight" in the average),
then the mass-weighted average reduces to
the count-weighted (ordinary, "straight") average:
##\displaystyle\frac{(1)x_1+(1)x_2+(1)x_3 }{(1)+(1)+(1)}=\frac{x_1+x_2+x_3 }{3}##.
)

LLT71
thanks guys!

## 1. What is the difference between average speed and average power?

Average speed is a measure of how fast an object moves over a certain distance, while average power is a measure of how much work is done in a certain amount of time. Average speed does not take into account the amount of work being done, while average power does.

## 2. Can average speed and average power be the same value?

No, average speed and average power are two different quantities and cannot be the same value. Average speed is measured in distance per time, while average power is measured in work per time. Therefore, the units and calculations for these two quantities are different.

## 3. How is average power related to average speed?

Average power is related to average speed through the equation power = force x velocity. This means that the amount of power being used is dependent on the force exerted and the velocity at which the object is moving. However, average speed only takes into account the distance and time of travel and does not consider the force or work being done.

## 4. Why is average power important in certain fields of science?

Average power is important in many fields of science because it helps to quantify the amount of work being done over a certain amount of time. In fields such as physics, engineering, and sports science, average power can provide valuable information about the efficiency and performance of a system or individual.

## 5. How can one accurately calculate average speed and average power?

To calculate average speed, divide the total distance traveled by the total time taken. To calculate average power, divide the total work done by the total time taken. It is important to use the correct units for distance, time, and work to ensure accurate calculations. Additionally, taking multiple measurements and averaging them can also improve the accuracy of these calculations.

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