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1. In the following expressions, x and y represent lengths or positions, v represents a velocity,...

1. In the following expressions, x and y represent lengths or positions, v represents a velocity, a represents acceleration, t represents a time, m is mass, and k has the value 2m?1. Use dimensional analysis to identify the invalid relationships: (a) vf = vi+ax, (b) y = (2m) cos(kx), (c) mat = mvx, (d) 2 ln(va=vb) = 6 sin(tb=ta).

2. A certain particle's position x at a time t is given by x = ka^mt^n, where k, m, and n are dimensionless constants and a and t represent acceleration and time, respectively. Find (i.e., algebraically solve for) the only permissible values for m and n rendering a valid expression. Is it possible to determine the value of k? Note: Do not merely substitute values for m and n to verify that certain values work. Solve for the values to show that only these work.

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