Which correctly relates the kinetic energy of the balls in the table above?

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 ?

Tall pacific coast redwood trees can reach heights of about 100 m. if air drag is negligibly small, how fast is a sequola cone moving when it reaches the ground f it dropped from the top of a 100 m tree?

Suppose that 27 j of work is needed to stretch a spring from its natural length of 6 m to a length of 9 m. (a) how much work is needed to stretch the spring from 12 m to 14 m? j (b) how far beyond its natural length will a force of 78 n keep the spring stretched?