In which way does stephen hawking use mathematics in his work?

Agas contained within a piston-cylinder assembly undergoes three processes in series: process 12: compression with pv= constant from 1 bar and 1 liter to 4 bar. process 23: constant pressure expansion to 1 liter. process 31: constant volume calculate the pressure and volume at each state, and sketch the processes on a p-vdiagram labeled with pressure and volume values at each numbered stat

Which sound characteristic is not affected by the relative motion of an object

An object with a mass of 1.5 kg changes its velocity from + 15 m/s to +22 m/s during a time interval of 3.5 seconds. what impulse was delivered to the objects?