Distance covered under variable acceleration

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SUMMARY

The discussion focuses on calculating distance under variable acceleration, specifically when acceleration is a function of velocity, as seen in electric-powered vehicles. The equation presented is a=Kv+C, leading to the differential equation mv(dv/dx)=Kv+C. By assuming constants for m, K, and C, participants suggest using separation of variables to solve for velocity and subsequently distance. The derived formulas for velocity and distance are v=C/K*(exp(K*t)-1) and x=C/K*(exp(K*t)/K-t), respectively.

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  • Knowledge of variable acceleration concepts
  • Basic physics principles related to motion
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Students and professionals in physics, engineering, and automotive design who are interested in understanding motion under variable acceleration conditions.

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Is it possible to find the distance covered in a certain time when acceleration depends on velocity, such as an electric-powered vehicle might do??
Acceleration := K*velocity + Const
 
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a=Kv+C

a=mv(dv/dx)

mv(dv/dx)=Kv+C

you would need to solve that equation, m,K and C are constants most likely by separation of variables.
 
Assuming K and C are constants, you can integrate to find v, then integrate to find x.
In this case, assuming starting from stand still, v=C/K*(exp(K*t)-1)
x = C/K*(exp(K*t)/K-t)
 

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