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What I was doing wrong was putting manufacturer-provided motor torque directly into the formulas; actually the overall gear ratio must be taken into account, and it results from data taken around on internet that for electric vehicles it is =~8 (dimensionless). Hence the proper expression to use for $v_f tanh(\frac{F}{mv_f} t)$ is not $v_f ...


0

I am adding another answer in order to show the steps needed to solve such problems in the general sense. An acceleration run is split into parts of differing acceleration domains. Given a starting condition for time, distance, speed, acceleration of $t_0, x_0, v_0, a_0$ here is what you can do Constant Torque with Air Drag $t=t_0 \rightarrow t_1$, $v=v_0 ...


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There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here, but for some reason I am not allowed to link to it normally: http://211.144.68.84:9998/91keshi/Public/File/34/482-7386/pdf/nature10779.pdf) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump ...


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You have to split the time domains into the gears needed to reach 60mph. For each gear, there have to be assumptions on the power delivery of the car. Typically 1st gear is traction limited, so you can assume constant acceleration up to the speed where peak power occurs. The relationship between power speed and acceleration is $P(v) = m \,v\, a(v)$. So run ...



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