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 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 m/s b. 0 #9 2.7 min # h 881 km/h #11 55 km/h 0

Linear Motion: Acceleration a = Δv = v f – v i t t Where a is acceleration v f is final velocity v i is initial velocity t is time Unit m/s 2 or m/s/s

Acceleration Practice #14. Ans: 5.2 s

Kinematics: 1-D 3 equations: v = v o + at x = x o + v o t + ½at 2 v 2 = v o 2 + 2a(x - x o ) With constant acceleration Like gravity

Equation 1 v = v o + at Where v is velocity v o is initial velocity a is acceleration t is time

Equation 1 Derivation a = Δv = v f – v i t t

Equation 2 x = x o + v o t + ½at 2 Where x is displacement x o is initial position v o is initial velocity t is time a is acceleration

Equation 3 v 2 = v o 2 + 2a(x - x o ) Where v is velocity v o is initial velocity a is acceleration x is displacement x o is initial position

Kinematics Summary EquationMissing Variable v = v o + atx x = x o + v o t + ½at 2 v v 2 = v o 2 + 2a(x - x o )t

Kinematics Example #26 Ans: a = -3.9 x 10 2 m/s 2, a = 40 g

Kinematics Example #37 Ans: t = 1.5 s

Kinematics Practice #38 #41

Kinematics Check #38 h = 13m # s

Kinematics Example #44 Ans: a. +/ m/s, b. t = s, 3.35 s, c. Up and down

Kinematics Practice #49

Kinematics Check #49 a s b m/s c m

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

Graphs: Important Aspects Labels Title Axes Measurements and units Slope Slope = Δy Δx Δx Area (under the curve)

Velocity vs. Time: Slope Slope = Δy = v = m/s = acceleration Δx t s

Velocity vs. Time: Area Area = ½ b h = (m/s) s = m = displacement

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 AREASLOPE m/s 2 * s = m/sm/s 2 / s = m/s 3 VelocityNot Useful

Velocity vs Time AREASLOPE m/s * s = mm/s / s = m/s 2 Displacement Acceleration

Displacement vs Time AREASLOPE m * s = m*sm / s = m/s Not Useful Velocity

Slope and Area Summary GraphAreaSlope Acceleration (m/s 2 ) vs Time (s)Velocity (m/s)Not Useful (m/s 3 ) Velocity (m/s) vs Time (s)Displacement (m)Acceleration (m/s 2 ) 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 m b. 500 m