HELP PROJECT DUE IN 3 HOURS Are there any ways we can improve cyclotrons to make them more efficient?

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 ?

An object is moving east, and it’s velocity changes from 65m/s to 25m/s in 10 seconds. which describes the acceleration?

Juan created a chart to him study for a test. which headings best complete the chart? x: transparent objects y: opaque objects x: opaque objects y: transparent objects x: high frequency waves y: low frequency waves x: low frequency waves y: high frequency waves