Arocket car is developed to break the land speed record along a salt flat in utah. however, the safety of the driver must be considered, so the acceleration of the car must not exceed 5g (or five times the acceleration of gravity) during the test. using the latest materials and technology, the total mass of the car (including the fuel) is 6000 kilograms, and the mass of the fuel is one-third of the total mass of the car (i. e., 2000 kilograms). the car is moved to the starting line (and left at rest), at which time the rocket is ignited. the rocket fuel is expelled at a constant speed of 900 meters per second relative to the car, and is burned at a constant rate until used up, which takes only 15 seconds. ignore all effects of friction in this problem.
find the final acceleration afinal of the car as the rocket is just about to use up its fuel supply. express your answer to two significant figures.

Study the diagram showing the range of temperature in the earth’s layers. which temperature most likely corresponds to the asthenosphere? 1,613°c 2,521°c 3,628°c 6,217°c

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation pv = 8.31t, where p is measured in kilopascals, v in liters, and t in kelvins. use differentials to find the approximate change in the pressure if the volume increases from 14 l to 14.6 l and the temperature decreases from 375 k to 370 k. (round the answer to two decimal places.)

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele