From: root@127.0.0.1.retro.com   
      
   >> Given a rocket or mass M ejecting as its exhaust a mass stream at a rate   
   >> m, and energy is imparted into this mass at a rate (power) of P, is it   
   >> possible to calculate the acceleration of the rocket?   
      
   > [2]   P = 0.5 * m * c^2 .   
      
   This is the equation I have problems with. It looks like you have taken the   
   definition of Kinetic Energy and differenciated both sides with respect to   
   time.   
   Is this a valid step here? The increase in kinetic energy when an   
   infinitesimal mass dm is accelerated out of the engine is clearly   
   dE=0.5*dm*c^2. This takes place over a time period T, which is an unknown   
   constant.   
   What [2] is saying, is that we replace T with dt, and then simply take   
   dE/dt = 0.5*(dm/dt)*c^2   
   (where my previous m=dm/dt)   
   This substitution of the unknown constant T with dt is what I'm having   
   problems with.   
      
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