WARNING: Extreme nerdiness occurring late on a Saturday night. Proceed at own risk.
I would do it in 3 phases, knowing your horse power at the 3 phases of your acceleration is easier than trying to integrate the power curve throughout (although it is possible with software).
I'd find your power in phase one, use that to determine your acceleration assume no drag at low speeds.
power in phase two, determine your kinetic friction, assume no air drag
power in in phase three, assume same kinetic friction, determine your air drag D=1/2(sigma =1)(rho @SL)(Surface area of your bike)(100 kph*1000/3600*3 (need it in ft/s))^2 or we could just assume that it's a factor of your power and say 0.15x your acceleration force which would be reasonable at those speeds.
Then you convert your power in all phases to a consistent accelerative force "pushing" you during those three phases and voila, you have your answer. Except...
If I were to simplify the question I'd say a block is accelerated in 3 phases, determine the distance covered. It spends 1s accelerated in the first phase, 1s accelerated in the second phase, 1.4s accelerated in the last phase. It's accelerative force is the average power in each phase/the velocity in each phase. We have average power, what we don't have is average velocity. there are 4 velocities, v1=0 when the block starts, v2 = ? at end of first phase v3 = ? . This obviously isn't going to work
I think at this point it needs to become a work energy problem. You know the power and the time it was applied for, so you have the energy expended in each phase. you could then determine your speed from energy for V2 because I assumed no drag at low speeds. Finding V3 we have an initial velocity (kinetic energy) plus potential energy (from the fuel burned, or the average power in phase 2 X the time it was applied for), we can determine the energy lost due to friction, to simplify we'll say it was 20% due to things like heat and friction, and we'll get a V3. and we know V4. So now we have velocities and times they were going at those speeds over an average. The three phase system might not be a perfect representation but oh well. I'll check my answer and see where I end up.
SOOOO, doing the math getting my values from:
http://www.motorcycle-usa.com/69331...o/2011-Yamaha-YZF-R6-Supersport-Shootout.aspx
I'd say 25 HP in phase 1, 50 HP in phase 2 and 95 HP in phase 3. That's ideal so the distance covered that I calculate will of course be ideal. 25 HP = 18.6KW = 18.6 KJ, 50 HP = 37.2 KW = 37.2 KJ, 95 HP = 70.2KW applied for 1.4 seconds so = 98.28 KW.
V2 = (18600/(1/2*250kg))^0.5 = 12.19m/s
V3 = ((18600 + 0.8*37200)/(0.5*250))^0.5= 19.66m/s
v4 (to check) = 18600 +0.8*(37200+98.28) = 31.8m/s (114 km/h, like I said, ideal situation. Not too bad I must say though given the amount of assumptions I made, using 27.8m/s)
Average distance covered in phase 1 = 6m
Average distance covered in phase 2 = 15.88m
Average distance covered in phase 3 = 33.22m
Total around 55 m, which I would say is a reasonable number. If I was doing it in real world scenarios, I'd have to take some more distance off at the end of those 3.4s due to rider error as well as tire slip etc. Also, this was based on the 3.4s time given. If I didn't have that time, I'd have done it differently, but then there was no guarantee that you'd be at 100kph at the end. All in all, I'd say this approximates it well enough.
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