Integrating nonconstant acceleration to give timeby Danny252 Tags: acceleration, integrating, nonconstant, time 

#1
Oct1710, 04:07 PM

P: 1

1. The problem statement, all variables and given/known data
Not specifically a homework assignment, but for a personal project  but it's almost entirely parallel with my Physics course at the moment, and is mostly a homeworkstyle question! I have an object acclerating due to a force, experiencing friction. Both the accelerating and friction forces depend on velocity. I would expect the result for v to tend to a certain value as time increases, similar to terminal velocity. I know this should involve integrating acceleration with respect to time  but the combination of questionable integration confidence and a cold mean I just can't fathom the next step. 2. Relevant equations Accelerating force = [tex]k/v[/tex] (decreases as v increases) Friction force = [tex]a + bv + cv^{2}[/tex] (increases as v increases) Total force = [tex]k/v  (a + bv + cv^{2})[/tex] Acceleration = [tex]\sum F/m[/tex] Velocity = [tex]\int a = \int (k/v  (a + bv + cv^2))/m[/tex] 3. The attempt at a solution My attempts at integration end with a 3rd degree polynomial: [tex](k\;ln(v)  (av + bv^2/2 + cv^3/3))/m[/tex] Whereas I expect t in the equation, and this does not lead to a limit (for sufficiently large values it gives negative speed). 


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