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Unformatted text preview: Math 23 B. Dodson Week 2b: 13.3 arc length, curvature 13.4 velocity, acceleration; 14.1 functions of several variables Week 2b Homework: 13.3 curvature (using vector algebra, Theorem 10) Problem 13.3.16 Use formula (9) to find the curvature of vector r ( t ) = < t 2 , 2 t, ln t > . (postponed) Week 2b Homework: 13.4 velocity, acceleration Problem 13.4.35: If vector r ( t ) = < e t , √ 2 t, e − t >, (a) Find velocity, acceleration and speed (from 13.4.11). (b) Find tangential and normal components of acceleration. Solution: (a) vector r ′ ( t ) = < e t , √ 2 ,- e − t >, vector r ′′ ( t ) = < e t , , e − t >, and | vectorv | 2 = ( e t + e − t ) 2 , so speed = e t + e − t . (b) We have ds dt = | vector r ′ ( t ) | = e t + e − t , so the tangential component a T of the acceleration vector vectora = vector r ′′ ( t ) = d 2 s dt 2 = d dt ( | vector r ′ ( t ) | ) = e t- e − t . 2 ....
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