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2. (From an old exam) A toy train travels counterclockwise around a circular track of radius R. Taking the center of the circle as the origin, the position vector of the train as a function of time is F(t) = R Cos (wt)i + Rsin (wt)ĵ where w is a constant. a) Find an expression for the train's velocity vector as a function of time.

2. (From an old exam) A toy train travels counterclockwise around a circular track of radius R. Taking the center of the circle as the origin, the position vector of the train as a function of time is F(t) = R Cos (wt)i + Rsin (wt)ĵ where w is a constant. a) Find an expression for the train's velocity vector as a function of time.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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2. (From an old exam) A toy train travels counterclockwise around a circular track of radius R. Taking the center of the circle as the origin, the position vector of the train as a function of time is F(t) = RCOS (wt)i + R sin (wt)ĵ where is a constant. a) Find an expression for the train's velocity vector as a function of time. b) Find an expression for the train's speed at any given time. Simplify it as much as you can. (Recall that cos² 0+ sin² 0 = 1, for any 0.) c) Your result for the speed in part (b) should be a constant. What does this imply about the train's acceler- ation? d) Find an expression for the train's acceleration vector as a function of time. Is it consistent with your answer to part (c)? (To check this, try sketching the two vectors at a couple of different times.)
Transcribed Image Text:2. (From an old exam) A toy train travels counterclockwise around a circular track of radius R. Taking the center of the circle as the origin, the position vector of the train as a function of time is F(t) = RCOS (wt)i + R sin (wt)ĵ where is a constant. a) Find an expression for the train's velocity vector as a function of time. b) Find an expression for the train's speed at any given time. Simplify it as much as you can. (Recall that cos² 0+ sin² 0 = 1, for any 0.) c) Your result for the speed in part (b) should be a constant. What does this imply about the train's acceler- ation? d) Find an expression for the train's acceleration vector as a function of time. Is it consistent with your answer to part (c)? (To check this, try sketching the two vectors at a couple of different times.)
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