In drag racing circles there are several formulas that people use to estimate th

Question

In drag racing circles there are several formulas that people use to estimate the quarter mile time that a car is capable of based on its power and weight. Possibly the earliest of these formulas is;
1 ElapsedTime = 6.29(Weight/HP)^(1/3)

(Ref:- http://www.stealth316.com/2-calc-hp-et-mph.htm)

Where the weight of the car is expressed in Pounds (lb) and HP is the power output of the car in Horse Power. Unit conversions are as follows; 1kg = 2.2lb, and 1kW = 1.35hp.

Convert the empirical formula above into SI units by calculating a new value for the coefficient out the front of the expression with weight expressed in kg and power expressed in kW.

**** I found the coefficient to be 7.288069199 (kg/kW)^(1/3), but I am uncertain if I have used the correct method to determine this (I substituted and rearranged) or whether or not I have used the method appropriately .

Explanation / Answer

1 Kg = 2.2 lb => 1 lb = 0.4545 kg 1 KW = 1.35 HP => 1HP = 0.741 KW 1 ElapsedTime = 6.29(Weight/HP)^(1/3) = 6.29 * (1 lb/1 HP)^(1/3 = 6.29(0.4545 Kg/0.741 KW)^(1/3) = 6.29*(0.4545/0.741)^(1/3) (Kg/KW)^(1/3) =6.29*0.85 (Kg/Kw)^(1/3) 1 ElapsedTime = 5.345 (Kg/Kw)^(1/3)

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