Quote:
This is Newtons Second Law: Acceleration is proportional to Force. More commonly written as Force = Mass x Acceleration.
This can be rewritten as a=F/m.
acceleration is change in velocity over time (v-u)/t
(v-u)/t = F/m
t=m(v-u)/F
v-u is constant because we are talking 0-60 time.
Then you have to play with some constants to convert from SI units to the everyday american ones and you end up with.
time = mass / force * some constant.
Which is exactly the formula you gave.
Phil.
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You are absolutely right Phil, it is pure physics. For some reason I never thought about it myself. Now that I did, I am very skeptical about it being Newton¡s Second Law, here is why.
From your formula t = mass / Force * constant. However you never specified what force is applied to the car? I am assuming it is Mass * Gravity? Plus, the (v - u) should not be constant, because it is change in velocity according to your derivation. Thus, it is delta V. Then the formula follows ==»
Time = (mass * V)/(mass * acceleration), or if we are taking units as follows:
Time = seconds = s
Mass = kilograms = kg
Distance = meters = m
Then s = (kg * m/s) / (kg * m/s^2) = seconds. That is what suppose to happen I believe. However, when you substitute everything, as in mass of the car, gravitational acceleration, and change in velocity, which in this case, 0-60mph or (0-26.6 m/s)/2, then the answer that we get is totally unrelated to anything, because then it won¡¦t depend on the mass of the car at all.
So here is my solution to this rather complicated problem:
Ok, taking the original formula: time = mass / bhp * constant.
Now, using units:
s = kg / (((kg * m)/s^2) * m/s) * C,
where bhp or hp = (((kg * m)/s^2) * m/s) = N *m/s = J/s = Watt
Therefore when simplified: s = s^3/(m^2 * C), which is apparently the formula that has to work, however for it to work, constant C has to have units of (s^2/m^2). And again, if you look at it, mass of the car is being canceled out, which is not suppose to happen. So my guess is, that the constant C has also be some sort of Force of gravity or frictional force for this formula to work properly, because otherwise it just does not make any sense.
How else would you divide kilograms/ horsepower * constant to get a time in seconds?