Review and Announcements

• Tatiana Brusentsova is the Teaching Assistant/Grader.

• My office hours will take place in Room 402 of the Physics Department.

• Make sure you are using WebAssign by the end of the week! Homework #1 due Monday.

Chapter 2: One-Dimensional Kinematics

• Outline• 2-1 Position, Distance, and Displacement• 2-2 Average Speed and Velocity• 2-3 Instantaneous Velocity• 2-4 Acceleration• 2-5 Motion with Constant Acceleration• 2-6 Applications of the Equations of Motion• 2-7 Freely Falling Objects

Major Concepts

• Position, distance and displacement• Speed and velocity

– Average– Instantaneous– Constant

• Acceleration– Average– Instantaneous– Constant

• Graphs of position versus time, velocity versus time, and acceleration versus time

• Equations of motion with constant acceleration• Free fall

Warning Areas:Speed vs. VelocityDistance vs. DisplacementConstant Velocity vs. Constant Acceleration

Distance and displacement

• Displacement is the net change in position from beginning to end of a journey

• Distance is the total amount of change in position, including re-tracing your steps on the journey.

Physics uses common terms in technical ways.

Figure 2-2One-Dimensional Coordinates

Try some examples…

Speed and Velocity

• Speed is the distance traveled in a period of time. It is a “scalar” (number only).

• Velocity is the displacement in a period of time. It is a “vector” (number and direction).

Distance and displacement

What is the displacement at 1s, 2s, 3s, 4s?What is the distance traveled at 1, 2, 3, 4s?

What is the average speed?

1. Greater than 40 mph.

2. Less than 40 mph.

3. Equal to 40 mph.

What is the average speed?

1. Greater than 40 mph.

2. Less than 40 mph.

3. Equal to 40 mph.

Problem solving:-draw a picture-label all quantities-identify “unknown”-write down relationships (formulas), working backwards from unkown to known-find a formula for the unknown-plug in the numbers

1

11

21

V

XT

TTTT

XVavg

Etc.

Example 2-2Sprint Training

Compare the average speed, and average velocity.

Figure 2-4Motion Along the X Axis Represented with an x-Versus-t Graph

Figure 2-5aAverage Velocity on an x-Versus-t Graph

Figure 2-6Constant Velocity on an x-Versus-t Graph

Figure 2-7Instantaneous Velocity

Figure 2-8Graphical Interpretation of Average and Instantaneous

Velocity

Our first formula!

If the velocity is constant, then the average velocity is the same as the instantaneous velocity.

T

XXV

TTTT

XXX

VT

XVAVG

0

0

0

Rearranging:

VTXX 0

Acceleration

• Acceleration is the change in velocity per unit time

• The average acceleration is the change in velocity per change in time. It is a vector quantity.

Figure 2-9v-Versus-t Plots for Motion with Constant Acceleration

Our second formula!

For constant acceleration…

atvv

vvat

t

vv

tt

vv

t

va

0

0

0

0

0

Velocity versus time produces a straight line graph, if acceleration is constant.

Figure 2-10Graphical Interpretation of Average and Instantaneous

Acceleration

Example 2-3An Accelerating Train

Cars Accelerating or Deceleratingwhich picture matches which graph?

1

2

3

4

Figure 2-13aThe Average Velocity

Definition: change in velocity divided by time.

Special case: Constant acceleration

Example 2-6Put the Pedal to the Metal

Figure 2-16Velocity as a Function of Position for the Ranger in Example 2-8

Notice that ½ the speed is lost in last ¼ of stopping distance.

CONSTANT DECELERATION

Example 2-9aCatching a Speeder

Q: How many mph?

Table 2-4Constant-Acceleration Equations of Motion

Variables Related Equation Number

Velocity, time, acceleration

v = v0 + at 2-7

Initial, final, and average velocity

vav = ½(v0 + v) 2-9

Position, time, velocity

x = x0 + ½(v0 + v)t 2-10

Position, time, acceleration

x = x0 + v0t + ½ at2 2-11

Velocity, position, acceleration

v2 = v02 + 2a(x – x0) = v0

2 + 2ax 2-12

Figure 2-22Problem 2-3

Figure 2-25Problem 2-17

Figure 2-26Problem 2-21

Find the average velocity for each segment of the “walk”, and for the total “walk”.

Now, compare DISPLACEMENT and DISTANCE.Compare, average VELOCITY and SPEED.

Figure 2-28Problem 2-32

What is the average acceleration for each segment, what is the average acceleration for the whole motorcycle ride?

Figure 2-29Problem 2-33

CAREFUL!

What is the displacement for each segment of the graph shown?

Problem solving:1. Draw a picture (given)2. What are they asking for?3. What is given?4. What are the mathematical relationships?