By definition, an electric field is accelerating the charge in the direction of decreasing electric potential. Hence, the charge's kinetic energy (and therefore velocity) is increasing.
But you don't know the electric field and therefore the force. So how do you figure out the change in kinetic energy? Because you know the potential, which is equivalent information. Think about it in terms of conservation of energy. The proton loses electric potential energy in moving from point A to B, which means that it must gain exactly that amount of kinetic energy. And you know, from the diagram, exactly how much potential energy per unit charge is lost in going from A to B. NOW do you understand what calculations need to be carried out?
Physics is not about memorizing formulae, it's about understanding and applying concepts. We can teach you equations, but if you don't understand physics, you won't know which ones to use in which situations. ;-)