What does it mean if there is air neglect , is this affect on the body motion

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

Power can be defined as a. the distance over which work was done. b. how much work can be done in a given time. c. all the work in an given area. d. the energy required to do work.