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Question: Solving a kinematics problem

Question:Solving a kinematics problem

iarwain 12 Maple
October 29 2005
0
Hi, I want to solve a kinematics problem. I have the following DE: > eq1:=diff(v(t),t)+4.646e-4*v(t)^3-7.13e-3*v(t)^2-0.085*v(t)-2.82: Where v=v(t) is the speed and t the time. My goal is to get the space crossed in a period of time: from t=3.35 to t=4.77 (seconds). Additional info: v(3.35)=14.77 m/s v(4.77)=20.4 m/s I've tried solving this with Maple but I couldn't (I'm a Maple newbie). This is what I tried: 1) I isolate the v and dv terms equation, so that: dt=dv/(-4.646e-4*v^3+7.13e-3*v^2+0.085*v+2.82) 2) Then I integrate that to get the time is function of the speed, t=f(v). > eq2:=1/(-4.646e-4*v^3+7.13e-3*v^2+0.085*v+2.82): > int(eq2,v): 3) Then, as v=diff(s(t),t) I tried to isolate the s(t) terms to one side of the equation, in ordet to get s(t) (integrating it). But I find this very difficult. The result of int(eq2,v) is insane. Another thing I've thought about is to get v(t) by applying DE methods to eq1. That would be great. But I don't know how to do it. Any ideas? Thanks a lot!
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