A young girl gives her toboggan a push of 4.0 m/s up a hill. It slides up the hill slowing down at an acceleration of 8.0 m/s2 [down]. It comes to a stop and then slides back towards her speeding up at the same rate as it slowed down on the way up. If the girl has to run 48 m down the hill from where it first was pushed to get to where her sled stopped, find the elapsed time for the total journey.

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 ?

The difference between two numbers is 15. when twice the smaller number is subtracted from three times the larger number, the difference is 58.what is the larger number?

2kg of refrigerant 134a undergoes a polytropic process in a piston-cylinder assembly from an initial state of saturated vapor at 2 bar to a final state of 12 bar, 80 degree c. a)determine the work for the process in kj. b)sketch the process on a p-v diagram.