Why is velocity squared in kinetic energy and mass multiplied by 1/2?

I) a gas contained within a piston-cylinder assembly undergoes two processes, a and b, between the same end states, 1 and 2, where p1 = 10 bar, v1 = 0.1 m3 , u1 = 400 kj and p2 = 1 bar, v2 = 1.0 m3 , u2 = 200 kj: ' process a: process from 1 to 2 during which the pressure-volume relation is pv = constant. ' process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to state 2. kinetic and potential energy effects can be ignored. for each of the processes a and b, a) sketch the process on a p-v diagram. b) evaluate the work, in kj. c) evaluate the heat transfer, in kj.(ans : qb,12 = -65.0 kj)