Warm-Up Pick up: A Giancoli book Far back left cabinet 1 of each paper at the front 3 Equation Sheets 1 Kinematics Multiple Choice 1 Kinematics Free Response.

Warm-Up

• Pick up:• A Giancoli book• Far back left cabinet

• 1 of each paper at the front• 3 Equation Sheets• 1 Kinematics Multiple Choice• 1 Kinematics Free Response

• I will be absent Friday

Kinematics: 1-D

Today’s Problems

• Giancoli, Chapter 2

•5, 7, 9, 10, 11, 14, 17, 26, 37, 38, 39, 41, 44, 49, 51, 52, 53, 56

Kinematics

• Kinematics• Study of motion

• 1-Dimensional• Horizontal (x) or Vertical (y)

• 2-Dimensional• Horizontal and Vertical simultaneously• Next time

Linear Motion: Review• Distance• Length of the path travelled

• Displacement• Overall change in position

Displacement

Distance

Linear Motion: Review

• Speed• Based on distance

• Velocity• Based on displacement• What happens if you travel in a complete circle?• Velocity = 0

Linear Motion: Velocity

• Remember:

v = x t

• Where• v is velocity• x is displacement• t is time

• Unit• m/s

Linear Motion Example

(#5, pg. 42)

• You are driving home from school steadily at 65 mph for 130 miles. It then begins to rain and you slow to 55 mph. You arrive home after driving 3 hours and 20 minutes.

• a. How far is you hometown from school?• 203 miles

• b. What was your average speed?• 62 mi/h

Linear Motion Practice

• #7• #9• #10• #11

Linear Motion Check

• #7• a. 4.29 m/s• b. 0

• #9• 2.7 min

• #10• 4.43 h• 881 km/h

• #11• 55 km/h• 0

Linear Motion: Acceleration

a = Δv = vf – vi

t t

• Where• a is acceleration• vf is final velocity

• vi is initial velocity• t is time

• Unit• m/s2 or m/s/s

Acceleration Practice• #14.

• Ans: 5.2 s

Kinematics: 1-D

• 3 equations:

v = vo + at

x = xo + vot + ½at2

v2 = vo2 + 2a(x - xo)

• With constant acceleration• Like gravity

Equation 1

v = vo + at

• Where• v is velocity• vo is initial velocity• a is acceleration• t is time

Equation 1 Derivation

a = Δv = vf – vi

t t

Equation 2

x = xo + vot + ½at2

• Where• x is displacement• xo is initial position

• vo is initial velocity• t is time• a is acceleration

Equation 3

v2 = vo2 + 2a(x - xo)

• Where• v is velocity• vo is initial velocity• a is acceleration• x is displacement• xo is initial position

Kinematics Summary

Equation Missing Variablev = vo + at x

x = xo + vot + ½at2 v

v2 = vo2 + 2a(x - xo) t

Kinematics Example• #26

• Ans: a = -3.9 x 102 m/s2, a = 40 g

Kinematics Example• #37

• Ans: t = 1.5 s

Kinematics Practice

• #38• #41

Kinematics Check

• #38• h = 13m

• #41• 5.22 s

Kinematics Example• #44

• Ans: a. +/- 12.8 m/s, b. t = 0.735 s, 3.35 s, c. Up and down

Kinematics Practice

• #49

Kinematics Check

• #49• a. 5.33 s• b. 40.2 m/s• c. 89.7 m

Kinematics and Graphs• Let’s examine a Velocity vs. Time graph:

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

Velocity vs Time

Time (s)

Velo

city

(m/s

)

Graphs: Important Aspects

• Labels• Title• Axes Measurements and units

• Slope• Slope = Δy

Δx

• Area (under the curve)

Velocity vs. Time: Slope

• Slope = Δy = v = m/s = acceleration Δx t s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

Velocity vs Time

Time (s)

Velo

city

(m/s

)

Velocity vs. Time: Area

• Area = ½ b h = (m/s) s = m = displacement

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

Displacment vs Time

Time (s)

Velo

city

(m/s

)

Slope and Area

• These will be very useful throughout the year

• Slope• Vertical .

Horizontal• Divide the units

• Area• Base times height• Multiply the units

Acceleration vs Time

0 10

1

Acceleration vs Time

Time (s)

Acce

lera

tion

(m/s

2)

AREA SLOPE

m/s2 * s = m/s m/s2 / s = m/s3

Velocity Not Useful

Velocity vs Time

AREA SLOPE

m/s * s = m m/s / s = m/s2

Displacement Acceleration0 1

0

1

Velocity vs Time

Time (s)

Velo

city

(m/s

)

Displacement vs Time

AREA SLOPE

m * s = m*s m / s = m/s

Not Useful Velocity0 1

0

1

Displacement vs Time

Time (s)

Disp

lace

men

t (m

)

Slope and Area SummaryGraph Area Slope

Acceleration (m/s2) vs Time (s) Velocity (m/s) Not Useful (m/s3)

Velocity (m/s) vs Time (s) Displacement (m) Acceleration (m/s2)

Displacement (m) vs Time (s) Not Useful (m*s) Velocity (m/s)

These are definitely not the only cases

Ex. Force vs. displacement

Instantaneous vs. Average

• Displacement vs Time (x vs t) graph• Average velocity• v = Δx

t• x’s and t’s from graph

• Instantaneous velocity• Velocity at one particular time• Line tangent to that time

Graphing Example• #39

Graphing Example• #51

Graphing Practice

• #52• #53• #56

Graphing Check• #52• a. t = 0 to 17 s• b. t = 28 s• c. t = 38 s• d. Both directions

• #53• a. t = 50 s• b. t = 90 s to 107 s• c. t = 0 to 20 s, and t = 90 to 107 s• d. t = 75 s

• #56• a. 1700 m• b. 500 m