Physics 114A - MechanicsLecture 3 (Walker: 2.4-5)Velocity & Acceleration

January 6, 2011

Physics 114A - MechanicsLecture 3 (Walker: 2.4-5)Velocity & Acceleration

January 6, 2011

John G. CramerProfessor Emeritus, Department of Physics

B451 PABjcramer@uw.edu

January 6, 2012 Physics 114A - Lecture 3 2/19

AnnouncementsAnnouncements Homework Assignments #1 is now available on

WebAssign and is due at 11:59 PM on Thursday, January 12. Assignment #2 is also posted and is due at 11:59 PM on Thursday, January 19. So far 172/216 WebAssign accounts.

Obtain a H-iTT clicker from the University Bookstore. We will begin using them for credit next Monday. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 121/216 clickers are registered.

On January 20 we will have Exam 1. It will be 75% multiple choice and 25% free response. There will be assigned seating. If would like a left-handed seat, an aisle seat, or a front-row seat, send me E-mail with your preference.

January 6, 2012 Physics 114A - Lecture 3 3/19

Physics 114A - Introduction to Mechanics - Winter-2012

Lecture: Professor John G. Cramer

Textbook: Physics, Vol. 1 (UW Edition), James S. Walker

Week Date L# Lecture Topic Pages Slides Reading HW Due Lab

1

2-Jan-12 H1 New Year Holiday  

No Lab 1st week3-Jan-12 1 Introduction to Physics 12 21 Chapter 1  

5-Jan-12 2 Position & Velocity 8 22 2-1 to 2-3 No HW

6-Jan-12 3 Velocity & Acceleration 10 25 2-4 to 2-5  

2

9-Jan-12 4 Equations of Motion 9 20 2-6 to 2-7  

1-D Kinematics10-Jan-12 5 Vectors 8 24 3-1 to 3-3  

12-Jan-12 6 r, v & a Vectors 5 24 3-4 to 3-5 HW1

13-Jan-12 7 Relative Motion 3 18 3-6  

3

16-Jan-12 H2 MLK Birthhday Holiday  

Free Fall & Projectiles17-Jan-12 8 2D Motion Basics 5 19 4-1 to 4-2  

19-Jan-12 9 2D Examples 13 22 4-3 to 4-5 HW2

20-Jan-12 E1 EXAM 1 - Chapters 1-4  

Lecture Schedule (Part 1)

Lecture Schedule (Part 1)

We are here.

Velocity & Acceleratio

n

Velocity & Acceleratio

n

January 6, 2012 Physics 114A - Lecture 3 5/19

Graphical Interpretation of Average & Instantaneous

Velocity

Graphical Interpretation of Average & Instantaneous

Velocity

January 6, 2012 Physics 114A - Lecture 3 6/19

Velocity & SlopeVelocity & Slope

The position vs. time graph of a particle moving at constant velocity has a constant slope.

The position vs. time graph of a particle moving with a changing velocity has a changing slope.

3.0 s

4.5 m

slope = velocity = 4.5 m/3.0 s = 1.5 m/s

January 6, 2012 Physics 114A - Lecture 3 7/19

Constant AccelerationConstant Acceleration

0 0 av x x x xv v v v a t

av if is constantx x xa a a

Acceleration characterizes the change in velocity with time: v/t. If the acceleration is constant, then the velocity is changing at a constant rate. Graphically, if we plot the velocity vs. time, it will fall on a straight line with a slope determined by the acceleration.

January 6, 2012 Physics 114A - Lecture 3 8/19

AccelerationAcceleration

, , (so t)fx ixxav x x av x

f i

v vva v a

t t t

0( ) lim xx

t

va t

t

Average acceleration:

Instantaneous acceleration:

Acceleration units: (m/s)/s = m/s2

January 6, 2012 Physics 114A - Lecture 3 9/19

Position, Velocity, & Acceleration

Position, Velocity, & Acceleration

Velocity negative;acceleration negative.

Velocity positive;acceleration zero.

Velocity positive;accelerationnegative.

Velocity positive;acceleration positive.

Velocity zero;acceleration zero.

January 6, 2012 Physics 114A - Lecture 3 10/19

AccelerationAcceleration

Average acceleration:

Eqn. (2-5)

January 6, 2012 Physics 114A - Lecture 3 11/19

Graphical Interpretation of Average and Instantaneous Acceleration:

AccelerationAcceleration

January 6, 2012 Physics 114A - Lecture 3 12/19

Example: An Accelerating Train

Example: An Accelerating Train

A train moving in a straight line with an initial velocity of 0.50 m/s accelerates at 2.0 m/s2 for 2.0 s, coasts with zero acceleration for 3.0 s, and then accelerates at -1.5 m/s2 for 1.0 s.(a) What is the final velocity vf of the train?(b) What is the average acceleration aav of the train?

2(3.0 m/s) (0.5 m/s)0.42 m/s

(6.0 s) (0 s)f i

avf i

v vva

t t t

1 1 2 2 3 3

2 2 2(0.50 m/s) (2.0 m/s )(2.0 s) (0 m/s )(3.0 s) ( 1.5 m/s )(1.0 s)

3.0 m/s

f i iv v v v a t a t a t

January 6, 2012 Physics 114A - Lecture 3 13/19

Acceleration (increasing speed) and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration:

Acceleration vs. Deceleration

Acceleration vs. Deceleration

Accelerating

Accelerating

Decelerating

Decelerating

January 6, 2012 Physics 114A - Lecture 3 14/19

Motion with Constant Acceleration

Motion with Constant Acceleration

If the acceleration is constant, the velocity changes linearly:

(2-7)

ConstantAcceleration

ChangingAcceleration1

02( )avv v v

Slope Constant Slope Changing

January 6, 2012 Physics 114A - Lecture 3 15/19

Motion with Constant Acceleration

Motion with Constant AccelerationVelocity vs. time: (2-7)

Average velocity: (2-9)

Position as a function of time:

(2-10)

(2-11)

Velocity as a function of position:

(2-12)

January 6, 2012 Physics 114A - Lecture 3 16/19

Motion with Constant Acceleration

Motion with Constant AccelerationThe relationship between position and time

follows a characteristic curve.

Parabola

January 6, 2012 Physics 114A - Lecture 3 17/19

Motion with Constant Acceleration

Motion with Constant Acceleration

January 6, 2012 Physics 114A - Lecture 3 18/19

A park ranger driving at 11.4 m/s in back country suddenly sees a deer “frozen” in the headlights. He applies the brakes and slows with an acceleration of 3.80 m/s2.(a) If the deer is 20.0 m from the ranger’s car when the brakesare applied, how close doesthe ranger come to hittingthe deer?(b) What is the stoppingtime?

2 2 2 20

2

(0) (11.4 m/s)17.1 m

2 2( 3.80 m/s )

v vx

a

20.0 m 17.1 m 2.9 md

00 2

(11.4 m/s)0 3.00 s

( 3.80 m/s )

vv v at t

a

Example: Hit the Brakes!Example: Hit the Brakes!

Before Monday, read Walker Chapter 2.6 and 2.7.

Register for WebAssign to do homework (so far, 172/216). Homework Assignments #1 is now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 12. Assignment #2 is also posted and is due at 11:59 PM on Thursday, January 19.

Obtain a H-iTT clicker from the University Bookstore. We will begin using them for credit next Monday. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page (so far 121/216 registered). We’ll test them now.

End of Lecture 3End of Lecture 3