物理的問題 有關微積分的 motion

The body of mass m is moving horizontally with initial velocity V in a medium in which the
"retarding force" is proportion to the velocity. Find the velocity and displacement of the
body as a function of time.(At t=0.V=V.X=0)
就醬...我不太會寫方程式耶..

[ 本帖最後由 max1130 於 2007-12-25 11:03 編輯 ]

from F=dp/dt where p=mv, so F=d(mv)/dt=mdv/dt=-kv, where k is a proportional constant. Therefore, mdv/dt+kv=0==> v(t)=C1exp(-kt/m) because v(0)=V==> C1=V. So, v(t)=Vexp(-kt/m). If you want to find x(t), just use dx/dt=v(t) and initial condition x(0) and then solve it.