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 [email protected]
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