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Assuming you can dodge all protons that would impede your motion, and that they're all at rest, how fast would you accelerate?

Values used/assumed:

mass of proton = 1.67*10^-27 kg

mass of person = 68 kg

Force of step = 100 N

Time duration of step = 0.01 s

Using the impulse-momentum equation here: https://www.physicsforums.com/showthread.php?t=440335 for getting a new velocity from a force, and then numerically integrating over time, I get the horrible result that you would have moved 14km in 15 minutes of running.

That is, I'm saying:

[itex]v[t+1]=v[t]+F*dt/m_{you}[/itex]

Which doesn't include the mass of the proton, which it seems like it should, so I feel like I can't assume that force. It was taken from typical earth equations for kicking things, but I've seen that ion drives have forces in milliNewtons.

So for any of you bored and willing to appease my awful assumptions for the sake of curiosity, what am I doing wrong?