04spex1sam - takes a long way, as seen in question (a). 1...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 320 Sample First In-class Exam March 2, 2004 M´arton Bal´azs 1. Above a certain velocity, the acceleration of vehicles pulled by electric motors (streetcars, trains, trolleybuses, electric cars) can be approximated to be proportional to the inverse of the square of their speed. Assume hence, by neglecting friction and air resistance, that an elevated train traveling with speed v has acceleration d v d t = 100 v 2 in the meter-second system. (a) (20 points) If at time zero it passes the end of the platform with a speed of 10 (m/s) (approximately 22.5 mi/h), then Fnd the distance (not the time!) in meters needed to accelerate to 20 (m/s) (approx. 45 mi/h), 30 (m/s) (approx. 67.5 mi/h) and 40 (m/s) (approx. 90 mi/h). (b) (15 points) Show that its speed tends to inFnity as t → ∞ . In other words, neglecting friction and air resistance, an electric vehicle accelerates to arbitrary large speeds, just it
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: takes a long way, as seen in question (a). 1 2. (30 points) Solve the initial value problem d y d x + 2 xy = x e-x 2 , y (0) = 1 . 2 3. For d y d x = sin y cos y (a) (15 points) Sketch, roughly, a direction feld and classiy the critical points. (b) (10 points) Determine, rom your sketch, the asymptotic behavior o the solution or y (0) = 1 as t . 3 4. Solve the system 3 x 1 + x 2 + 2 x 3 = 4 x 2-x 3 = 4-2 x 1 + 4 x 2-x 3 = 11 using (a) (20 points) Gauss-Jordan elimination, (b) (20 points) Cramers method. 4 5. Given the matrix A = 1 2 p-1- 3 3-1 P , (a) (15 points) compute A 2 and A 3 . (b) (15 points) Based on these results, determine the matrices A-1 and A 2004 . 5...
View Full Document

This note was uploaded on 08/11/2008 for the course MATH 475 taught by Professor Balazs during the Fall '05 term at Wisconsin.

Page1 / 5

04spex1sam - takes a long way, as seen in question (a). 1...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online