A train is traveling south at constant speed 12.0 m/s. Then the brakes are applied & it slows down with a constant acceleration to a speed of 3.00 m/s in a time of 9.00 s. (a) Draw a graph of speed versus time for a 12-s interval (starting 2 s before the brakes are applied and ending 1 s after the brakes are released).
(b) What is the acceleration of the train during the 9.00-s interval?
(c) How far does the train travel during the 9.00 s?

Identify the theory that can be used to explain each phenomenon. answers diffraction: wave theory interference: wave theory reflection: both particle and wave theories refraction: both particle and wave theories

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

A47.2 g block of copper whose temperature is 480 k is placed in an insulating box with a 91.8 g block of lead whose temperature is 200 k. (a) what is the equilibrium temperature of the two-block system? (b) what is the change in the internal energy of the two-block system between the initial state and the equilibrium state? (c) what is the change in the entropy of the two-block system? the heat capacities of copper and lead are 386 j/kg·k and 128 j/kg·k, respectively.