Homework2-help

# Homework2-help - Homework2 help 2.28. Visualize: Solve: We...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework2 help 2.28. Visualize: Solve: We will determine the objects velocity using graphical methods first and then using calculus. Graphically, ( ) v t v = + area under the acceleration curve from 0 to t . In this case, 0 m/s. v = The area at each time t requested is a triangle. 0 s t = ( 0 s) 0 m/s v t v = = = 2 s t = 1 ( 2 s) (2 s)(5 m/s) 5 m/s 2 v t = = = 4 s t = 1 ( 4 s) (4 s)(10 m/s) 20 m/s 2 v t = = = 6 s t = 1 ( 6 s) (6 s)(10 m/s) 30 m/s 2 v t = = = 8 s t = ( 8 s) ( 6 s) 30 m/s v t v t = = = = The last result arises because there is no additional area after 6 s. t = Let us now use calculus. The acceleration function a ( t ) consists of three pieces and can be written: 2.5 0 s 4 s ( ) 5 30 4 s 6 s 6 s 8 s t t a t t t t = - + These were determined by the slope and the y-intercept of each of the segments of the graph. The velocity function is found by integration as follows: For 0 t 4 s, 2 2 ( ) ( 0 s) ( ) 0 2.5 1.25 2 t t t v t v t a t dt t = = + = + = This gives 0 s t = ( 0 s) 0 m /s v t = = 2 s t = ( 2 s) 5 m /s v t = = 4 s t = ( 4 s) 20 m /s v t = = For 4 s 6 s, t 2 2 4 4 5 ( ) ( 4 s) ( ) 20 m/s 30 2.5 30 60 2 t t t v t v t a t dt t t t - = = + = + + = - +- This gives: t = 6 s ( 6 s) 30 m/s v t = = For 6 s 8 s, t 6 ( ) ( 6 s) ( ) 30 m/s 0 m/s 30 m/s t v t v t a t dt = = + = + = This gives: t = 8 s ( 8 s) 30 m/s v t = = 2.56. Model: The cars are represented as particles. Visualize: Solve: (a) Ann and Carol start from different locations at different times and drive at different speeds. But at time 1 t they have the same position. It is important in a problem such as this to express information in terms of positions (that is, coordinates) rather than distances. Each drives at a constant velocity, so using constant velocity kinematics gives A1 A0 A 1 A0 A 1 A0 ( ) ( ) x x v t t v t t = +- =- C1 C0 C 1 C0 C0 C 1 ( ) x x v t t x v t = +- = + The critical piece of information is that Ann and Carol have the same position at...
View Full Document

## This note was uploaded on 04/18/2010 for the course PHYS ? taught by Professor Zhou during the Spring '10 term at Georgia State University, Atlanta.

### Page1 / 7

Homework2-help - Homework2 help 2.28. Visualize: Solve: We...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online