A proton has mass 1.7 ✕ 10-27 kg. what is the magnitude of the impulse required to increase its speed from 0.991c to 0.994c?

Impulse is the equivalent to the force as the change in momentum, such that F*t = mv - mu

Since mass and speed is given, use the above right hand side formula mass, m = 1.7 x 10^27 kg initial velocity, u = 0.991 x (3 x 10^8) = 2.973 x 10^8 final velocity, v = 0.994 x (3 x 10^8) = 2.982 x 10^8

So the computation is:

Impulse = mv - mu

= [ (1.7 x 10^27) x (2.982 x 10^8) ] - [ (1.7 x 10^27) x (2.973 x 10^8) ] = (5.0694 x 10^35) - (5.0694 x 10^35) = 0