False.
The equation shows the power used. The slower one may be a more powerful runner, but was being lazy - you know “lazy” - like your thinking.
Power is work/time.
You don’t do work in your head, you do it in the real world. Power isn’t some imagined potential, or some measure of how fast you “could have” moved 150 lbs 100 yards.
Power is how fast you ACTUALLY moved 150 lbs 100 yards.
Energy is power x time.
Ever get an electric bill with how much power or energy you COULD HAVE USED for that month?? Does your power company bill you for how much you COULD HAVE used that month, or do they bill you for how much you ACTUALLY used?
Work = Force x Distance
Power = Work / Time
Energy = Power x Time
Therefor:
Energy = (Work/Time) x Time
Energy=((Force x Distance)/Time) x Time
They don’t do the same work.
Work is Force x Distance
And Force is Mass x Acceleration
Therefore Work is Mass x Acceleration x Distance
The distance is the same and we are assuming their mass is the same.
So the work that they do depends on how they accelerated. A quick initial acceleration followed by steady cruising will produce a different amount of work than a steady acceleration over the length of the race.
And the fact that they did not run at the same speed means that their acceleration was much different.
Lifting 100 lbs 3 feet is 300 ft-lbs of WORK, whether it takes you 1 second, or 10 seconds.
Power factors the time to give you the rate of work that you did, the more time means the lower the power. The work is always the same regardless of time. In this case the WORK is 300 ft-lbs of WORK!
Do you agree that the distance is given as d=1/2 * a * t^2 ?
The distance is 100 m
The mass is the same for both.
Time (t1) for runner 1 is 10 s
Time (t2) for runner 2 is 20 s
Assuming a steady acceleration for both:
100 = 1/2 * a1 * 10^2
a1= 2 m/s/s
100 = 1/2 * a2 * 20^2
a2= 0.5 m/s/s
Work = m * a * d
Work1 = m * 2 * 100 = m * 200
Work2 = m * 0.5 * 100 = m * 50
Since their mass is the same, runner 1 did 4 times the work of runner 2.
QED
My example involved transportation, which would save the object/person their time and energy (effort) in arriving at the desired destination.
Runners are their own vehicle… so to speak, but are incapable of interstellar running, but yes… runner 1 is the V8 of runners to runner 2’s V4.
In part, my point upthread too.
Light years, time and distance are components of the either/or world. Presumably anyway. So, which fulminating fanatic above comes closest to guiding us down the One True Path here?
On the other hand, even “standard science” exists within the ultimately mysterious – and some insist mystical – parameters of “the gap” and “Rummy’s Rule”. Not to mention all that weird speculation about reality/“reality” given the components of the quantum world.
Then this part. Pood admits there are no clear-cut scientific answers regarding such things as determinism. So, what of those who argue that, given their own understanding of it, this entire thread is unfolding into the future in the only possible manner in which it could. I’m typing these words because I was never able not to type them. You’re reading these words because you were never able not to read them. You think as you do about light years, time and distance only because your brain compels you to.
“No!”, screams pood, “that’s idiotic!!”
And he has the Regularity Theory to “prove” it.
This in and of itself precipitates mind-boggling conjectures.
Suppose next month the really, really, [b]really[/b] Big One strikes Earth. An asteroid immense enough to wipe out every single last one of us. No human beings left at all.
And suppose further that human beings are the only intelligent life form in the entire universe.
What then of light years, time and distance? What then of things like the Twin Paradox?
Cue God?
Which has been demonstrated, repeatedly, to be incorrect for more than a century.
_
I should have also added, that whether one travels 1LY/9Tkm in 1yr, or travels round the planet for a year, it’s still 1 year… it is specific variables at play, creating the conditions for the differences in distance travelled, and not time.
Do you agree that 1) there are many different types of definitions (e.g. ostensive definitions), and that 2) what amounts to a good definition is a realtive thing (relative to one’s goals, to one’s present knowledge and so on)?
I can accept that the definition that I provided is not satsifying to you. In that case, you would have to explain what kind of definition you are looking for and why.
Take me as an example. I can accept that “time is the measure of relative change” is a definition but I don’t find it to be a satisfying one for several reasons. One of the reasons is that what’s meant by the word “measure” is not particularly clear to me. For example, is that definition saying that the word “time” can be used to represent “5 minutes” text written down on a piece paper meant to to represent how long it took someone to do some task?
What does that mean? What does it mean that it declares that there is no “relativity”? Are you speaking of what James calls “relative change”? If so, feel free to define “relative change” and then we’ll see whether or not my definition forbids the existence of such a thing.
In any case, I am inclined to believe that it doesn’t deny the existence of anything (not even unicorns) for the simple reason that it is a definition – it is not a claim about reality. It’s merely a declaration that some word means something.
I beg to differ. I am not sure you understood what I said. James’s definition implies that if there is no change that there is no time. In other words, it prohibits the possibility of there being time when there is no change.
It is a description of how some people define the word “time” – James being one of them. And you can also say that such a definition is useful to certain ends – and perhaps more advantageous in certain ways than my own definition. But to say that it’s what every rational person is obliged to adopt? I don’t agree with that. Different ends require different concepts.
That is the distance that an object travels during a time of acceleration, not the total distance of 100 Meters.
In the example, it is assumed that the velocity is constant the entire race. There is no acceleration, the acceleration is zero.
Acceleration is the rate of change of velocity. In this simple example we assume the runners start the race at velocities of 5 m/s and 10 m/s, and those velocities remain constant the entire race. There is no change of velocity (acceleration.)
The distance is simply 100 Meters, or D=100 Meters
The time in your equation is for acceleration time, not the entire duration of time of travel.
See my Equations of Motion thread for a complete set of equations.
I think what you’re trying to say is that a V8 producing 50 lb-ft of torque at 5,000 RPM produces more power than a V4 producing 50 lb-ft of torque at 2,500 RPM.
But we both know that there are 4 cylinder engines that produce 500 HP and there are 8 cylinder engines that produce 250 HP, RIGHT? 
I’m using a constant acceleration to show you that the work is not the same for both runners. That’s the simplest example of my point.
If the velocity was constant then they would have already started the race running at full speed.
Your absurd case has no acceleration and therefore no work and no power.
I simply apply a constant acceleration over the entire race. Which is plausible. And it shows that work is not the same for the runners.
The work is exactly the same for both runners. I gave you an example that you ignored. Lifting 100 lbs 3 feet is 300 ft-lbs of work, whether it takes you 3 hours to lift it or 1 second to lift it. The work is lifting 100 lbs 3 feet, which is 300 ft-lbs of work. The acceleration has nothing to do with work. Acceleration is the rate of change of velocity. Work is force times distance. The force is 100 lbs, and the distance is 3 feet, for 300 ft-lbs of work. Velocity would require a time, but work has no time, it is simply 100 lbs 3 feet.
They did start the race at full speed. At t=1 second the fast runner was at the 10 meter mark, and the slow runner was at the 5 meter mark. That is constant velocity the entire race. Every second the fast runner moved 10 meters and the slow runner moved 5 meters. At t=.1 seconds the fast runner was at the 1 meter mark and the slow runner was at the .5 meter mark. They maintained those velocities the entire race. They did not change velocity the entire race, so the entire race there was no acceleration. ZERO!
Of course there was work and power. Are you trying to say that a car cruising at a constant 70 MPH isn’t doing work, and the engine isn’t producing power???
You are saying they were accelerating the entire race? So what was the velocity at t=1 for each of them? What was the velocity at t=5 for each of them?
MD, that’s just not true. You’re either overthinking or under thinking this.
It costs more energy simply to live a longer amount of time than a lesser amount of time.
- Both runners would save energy doing a lot less work if they just took the bus.
No energy is used or work is done if there is no acceleration - momentum continues without work.
That is a description of what is universal about time - it is not a description of what time is (a definition of “time”). It is like defining a “king” as “a king wears a crown” - that doesn’t tell you what a king is.
Time = the measure of relative change
That is a description of what time is - a definition. And “relative change” just means how much one thing has changed compared to how much something else changed. A clock changes at a fixed rate so that other changes (passing days, internet connections, runners, buses, and Motor’s mouth) can be measured. Time is a MEASURE (like length).
If something causes the measure to change - such as high velocity - then time has changed. That might or might not include a clock but the fact that a clock and all relative motion MUST change at extreme velocity (because extreme velocity has an upper limit) indicates that time itself changes - so NOT universal.
Ok, obsrvr,
I’m going to play ‘devils advocate here.
If C is the universal constant, how is anything moving faster or slower than anything else?
How does “time change”? It’s a bit absurd to say that, but let’s not get into that. How does one C go faster or slower than another C if it’s all C?
I was? I didn’t feel the need to specify… it was an analogy, not a sales pitch. 
…tho I did find the below out when helping someone choose which vehicle to buy… he obviously went for the vehicle with the most power and speed.
Actually, that is RIGHT ; ) …perhaps I should have stuck with the original analogy/example I was going to use, which was that of ‘runner 1 is the Lamborghini of runners to runner 2’s Skoda’, as… no explanation necessary with that one, as it’s self-explanatory.
Good. That’s what I thought.
But what does it mean to say that thing A has changed by X compared to thing B that has changed by Y?
What does it mean to say that the angle of the sweep hand on your clock has changed by 360 degress compared to your position in space that has changed by 5 meters?
I know what it means for a thing to change. I know what it means for the angle of a sweep hand to change by 6 degrees. I also know what it means for the position of an object in space to change by 5 meters. What I don’t understand is the “compared to” part.
Or perhaps I do?
There is a possibility that you’re basically saying that during the time it took your position in space to change by 5 meters, the angle of the sweep hand on your clock has changed by 360 degrees.
If that’s the case, isn’t your definition a bit circular?
Aren’t you trying to define time in terms of time?
In the standard ontology, as I understand it, time is a fundamental concept; and rather than being defined in terms of change, it is change that is defined in terms of time. Change is defined as a difference between two points in time. If I asked you to define the word “change”, I am not sure what you’d give me given that you can’t use my definition.