2. A student measured the length of a laboratory table as 4.5 m accurate to 0.1 of a meter, Find the absolute, relative and percentage errors in this measurement.​

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 ?

Athermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 10° f. after one-half minute the thermometer reads 60° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.) ° f how long will it take for the thermometer to reach 30° f? (round your answer to two decimal places.)

Awater slide of length l has a vertical drop of h. abby's mass is m. an average friction force of magnitude f opposes her motion. she starts down the slide at initial speed vi. use work-energy ideas to develop an expression for her speed at the bottom of the slide. then evaluate your result using unit analysis and limiting case analysis. express your answer in terms of the variables h, m, l, vi, f and appropriate constants. vf v f