No, forces are applied, power is an intrinsic property, so you might rather say "Given two movers with equal average power, one that goes twice as long also goes eight times as far"; however, this is also incorrect. The integral equation P = Int F*v*dt, says that power depends on resistive force. This is somewhat confusing when thinking of, say, a sprinter or a marathon runner because it isn't clear what the resistive force is. It is more complicated than you might guess: http://www.georgeron.com/2017/09/kipchoge-running-power-marathon.html If you want a high school problem to work out, here is one I wrote earlier this month: https://0x0.st/i14t.pdf --Brad On Mon, Apr 20, 2020 at 12:06 PM Bill Gosper <billgosper@gmail.com> wrote:
In[395]:= UnitConvert[Quantity[42, "Watts"], "Kilograms" "Meters"^2/"Seconds"^3]
Out[395]= Quantity[42, ("Kilograms" ("Meters")^2)/("Seconds")^3]
This seems to say: If you apply a given amount of power (to a freely moving object) for twice as long, you go eight times as far. —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun