Aproton has been accelerated from rest through a potential difference of -1000 v . part a what is the proton's kinetic energy, in electron volts?

We can apply the law of conservation of energy here. The total energy of the proton must remain constant, so the sum of the variation of electric potential energy and of kinetic energy of the proton must be zero:

which means

The variation of electric potential energy is equal to the product between the charge of the proton (q=1eV) and the potential difference ():

Therefore, the kinetic energy gained by the proton is

And since the initial kinetic energy of the proton was zero (it started from rest), then this 1000 eV corresponds to the final kinetic energy of the proton.