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automotive performance and calculus

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Did you know that automobile performance can be described by calculus? Newton's law of motion dF=m*dV and dP=V*df so that dP=m*V*dV or dP=m*d(V²) which is where m(V²)/2 comes from and why it's twice as hard to accelerate from 60 mph than 30 mph? Did you know that quarter-mile times and trap speeds can also be related by separating and integrating these same ordinary differential equations? I have attached a figure based on 106 car tests reported by a popular magazine. Calculus yields the quarter-mile time to be t=(9mX²/8P)^(1/3), which is very close to the regression obtained with Excel. The trap speed is V=(3PX/m)^(1/3), also close to what Excel comes up with. Mechanical engineers: PAY ATTENTION IN MATH CLASSES AND DON'T TRY TO AVOID THE TOUGH ONES.


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