Science question james and toby are running in a 100 m race. james' velocity is 10 m/s to the right and toby's velocity is 8 m/s to the right. which of the following statements is true? 1. james will finish the race before toby. 2. in a position time graph, james' slope would be steeper than toby's slope. 3. if toby runs at a constant velocity, the sizes of the arrows in a vector graph will all be the same. 4. all of the above.

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