5. an 8 kg shopping cart is pushed, causing it to accelerate by 4 m/s? how much force was used to
push the cart? use the equation below to calculate the answer.

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 ?

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20â°c throughout the year, while the walls of the room are nominally at 27â°c and 14â°c in the summer and winter, respectively. the exposed surface of a person in the room may be assumed to be at a temperature of 32â°c throughout the year and to have an emissivity of 0.90. the coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 w/m2 â‹…â‹… k. what is the ratio of the thermal resistance due to convection to the thermal resistance due to radiation in the summer? what is the ratio of thermal resistances in the winter

Ryan is examining the energy of the particles in a bar of gold. what is ryan most likely studying?