lec_week3

lec_week3 - MIT OpenCourseWare http://ocw.mit.edu 18.02...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 18.02 Lecture 6. Tue, Sept 18, 2007 Handouts: Practice exams 1A and 1B. Velocity and acceleration. Last time: position vector r ( t ) = x ( t ) + y ( t ) j [+ z ( t ) k ] . E.g., cycloid: r ( t ) = t sin t, 1 cos t . dr dx dy Velocity vector: v ( t ) = dt = dt , dt . E.g., cycloid: v ( t ) = 1 cos t, sin t . (at t = 0, v = 0: translation and rotation motions cancel out, while at t = they add up and v = 2 , 0 ). Speed (scalar): | v | . E.g., cycloid: | v | = (1 cos t ) 2 + sin 2 t = 2 2 cos t . (smallest at t = 0 , 2 , ... , largest at t = ). dv Acceleration: a ( t ) = . E.g., cycloid: a ( t ) = sin t, cos t (at t = 0 a = , 1 is vertical). dt Remark: the speed is | dr | , which is NOT the same as d | r | !...
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This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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lec_week3 - MIT OpenCourseWare http://ocw.mit.edu 18.02...

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