Exam (elaborations) TEST BANK FOR Elementary Mechanics and Thermodynamics By Prof. John W. Norbury (Solutions Manual)

CHAPTER 1. MOTION ALONG A STRAIGHT LINE 1. The following functions give the position as a function of time: i) x = A ii) x = Bt iii) x = Ct2 iv) x = Dcos !t v) x = E sin !t where A;B;C;D;E; ! are constants. A) What are the units for A;B;C;D;E; !? B) Write down the velocity and acceleration equations as a function of time. Indicate for what functions the acceleration is constant. C) Sketch graphs of x; v; a as a function of time. SOLUTION A) X is always in m. Thus we must have A in m; B in msec¡1, C in msec¡2. !t is always an angle, µ is radius and cos µ and sin µ have no units. Thus ! must be sec¡1 or radians sec¡1. D and E must be m. B) v = dx dt and a = dv dt. Thus i) v = 0 ii) v = B iii) v = Ct iv) v = ¡!D sin !t v) v = !E cos !t and notice that the units we worked out in part A) are all consistent with v having units of m¢ sec¡1. Similarly i) a = 0 ii) a = 0 iii) a = C iv) a = ¡!2Dcos !t v) a = ¡!2E sin !t