Physics - MechanicsLecture 2

Velocity and AccelerationSeptember , 2013

Physics 114A - Lecture 3 2/19

Physics 114A - Introduction to Mechanics - Winter-2012

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)

We are here.

Velocity & Acceleration

4/19

Graphical Interpretation of Average & Instantaneous Velocity

5/19

Velocity & 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

6/19

Constant 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.

7/19

Acceleration

, , (so t)fx ixx

av x x av x

f i

v vva v a

t t t

0( ) lim x

xt

va t

t

Average acceleration:

Instantaneous acceleration:

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

8/19

Position, Velocity, & Acceleration

Velocity negative;acceleration negative.

Velocity positive;acceleration zero.

Velocity positive;accelerationnegative.

Velocity positive;acceleration positive.

Velocity zero;acceleration zero.

9/19

Acceleration

Average acceleration:

Eqn. (2-5)

10/19

Graphical Interpretation of Average and Instantaneous Acceleration:

Acceleration

11/19

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

av

f 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

12/19

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

Acceleration vs. Deceleration

Accelerating

Accelerating

Decelerating

Decelerating

13/19

Motion with Constant Acceleration

If the acceleration is constant, the velocity changes linearly:

(2-7)

Constant

Acceleration

Changing

Acceleration1

02( )avv v v

Slope Constant Slope Changing

14/19

Motion with Constant Acceleration

Velocity 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)

15/19

Motion with Constant AccelerationThe relationship between position and time follows a characteristic curve.

Parabola

16/19

Motion with Constant Acceleration

17/19

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 2

0

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!