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Mathematics 317 Midterm #1: Monday, October 5, 2009 1. Do only two questions. Each question is of equal value. If you attempt more than two questions, only the first two will be marked.2. No notes, books or calculators are permitted. A data sheet is included separately. 3. Time Limit: 50 minutes 1. Let (trbe the position vector of a particle at time t. .,,rvavrv&&&&=====dtdsv(a) Show that the velocity of the particle satisfies the equation .Tvv(b) Show that the acceleration of the particle satisfies the equation NTva2vvκ+==&where κis the curvature, at time t, of the path traced out by the particle. (c) Let .)(rrA×=&tFind a condition for A(t) so that the motion is planar. 2. A particle’s position at time