An astronaut has left the international space station to test a new space scooter. her partner measures the following velocity changes, each taking place in a time interval 10.6 s . what are the average acceleration in each interval? assume that the positive direction is to the right.

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 ?

Why do electron microscopes have higher resolving power than light microscopes?

An object of dimensions 50 cm x 40 cm x 0.20 cm has a mass 60g. find its density in g/cm3 and kg/ m3