[sudhirj]

There's two different kinds of energy here - the kinetic energy of a moving thing hitting you in opposition is a problem. No way to capture that as far as I know - it's like running into a wall and asking how it can help you go faster.

But then there's e=mc^2, so if the stuff you're running into is the fuel source for your fusion engine (could be a fission engine, but unlikely you'll run into heavy atoms like Uranium or Plutonium) then you have an unlimited source of energy...

So maybe sort of? Running into things slows you down, but then you capture that mass and release the energy out of it to go faster... because of the nature of e=mc^2 you'll usually get more energy out of something if you convert its mass than what you lose by running into that mass.

[_factor]

I’m imagining a ship with a hole in it and a piece of fuel at the backside where the particles hit. It would slow you down first since you’re tethered to the particles, then the explosion would push you forward.

The issue is that the energy for that explosion comes from the slowing down of your ship, so it doesn’t work.

[sudhirj]

The energy that comes from a mass-energy conversion greatly exceeds kinetic energy losses.

For the same reason that the power of an atomic bomb does not depend on how fast you smash the sections together - it depends on how much mass is converted to energy in the resulting reaction.