This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: blue MATH 32A Exam 2 February 20, 2008 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (20 pts) 5 (20 pts) 2 (10 pts) 6 (20 pts) 3 (20 pts) 7 (20 pts) 4 (20 pts) TOTAL 2 PROBLEM 1 (20 Points) A particle travels along a path parametrized by a vector valued function r ( t ). Assume that at time t = 2, r (2) = h 1 , 2 , 2 i , r 00 (2) = h 2 , , 10 i Find the curvature of the path at t = 2. Answer : Solution: At t = 2: r 00 (2) = a T T + a N N We have a T T = r 00 (2) r (2) r (2) r (2) r (2) = h 2 , , 10 i h 1 , 2 , 2 i h 1 , 2 , 2 i h 1 , 2 , 2 i h 1 , 2 , 2 i = 18 9 h 1 , 2 , 2 i = h 2 , 4 , 4 i and v 2 = a N =  a N N  =  r 00 (2) a T T  = h 2 , , 10 i  h 2 , 4 , 4 i = h 4 , 4 , 6 i = 68 The square of the speed is v 2 =  r (2)  2 = 9 and thus v 2 = 9 = 68 It follows that = 68 9 3 PROBLEM 2 (20 Points) A particle travels along the curve y = x 3 . Assume units of meters and seconds. At a certain moment, the particle is located at the point...
View
Full
Document
This test prep was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.
 Winter '08
 GANGliu
 Math

Click to edit the document details