Chapter 2 Motion Along a Line Position Displacement

Chapter 2: Motion Along a Line • Position & Displacement • Speed & Velocity • Acceleration • Describing motion in 1 D • Free Fall • CQ: 1, 2, 3, 4. • P: 1, 13, 25, 27, 29, 47, 50.

Applications • • Destination times Design packing materials & road barriers Airbag deployment speed Simulations (movies & games) 2

Speed • Speed = rate of travel at a given moment of time • Distance traveled = total length of the curved path 3

Initial/Final Notation Same rules apply for all variables 4

Delta Notation called Displacement 5

Velocity (m/s) When Dt is small, Dx/Dt is the instantaneous velocity v. 6

Graphs • Wilson (12) x vs t • Giambattist (21) +, -, 0 accel. • area under v vs. t curve = displacement

Acceleration (m/s/s) If Dt is small, Dv/Dt is called the instantaneous acceleration and labeled “a”. 8

Ex. Car Acceleration from 10 m/s to 15 m/s in a time of 2. 0 seconds. In this class we only use average acceleration and often drop the “avg” notation from acceleration. 9

Velocity Formula 10

acceleration • Wilson (15) negative acceleration

Average Velocity with Uniform Acceleration • Uniform Acceleration = constant valued acceleration • During uniform acceleration, average velocity is halfway between vo and v: 12

Average Velocity Formula 13

Displacement Formula 14

V-squared Equation 15

Kinematic Equations with Constant Acceleration 16

Ex. Human Acceleration In the 1988 Olympics, Carl Lewis reached the 20 m mark in 2. 96 s (Bolt: 2. 87 s) 17

Ex: V 2 Equation Approximate Stopping Accelerations in m/s/s: Dry Road: ~ 9 (anti-lock) ~ 7 (skidding) Wet Road: ~ 4 (anti-lock) ~ 2 (skidding) At 60 mph = 27 m/s, what is the skid-to-stop distance on a wet road? 18

Scalars & Vectors • Scalar: size only • e. g. speed, distance, time • Vector: magnitude and direction • e. g. displacement, velocity, acceleration • In one-dimension the direction is determined by the + or – sign. • In two-dimensions, two numbers are required. 19

Motion Diagrams • Are velocity-position diagrams • More visual than a graph of x or v vs. time • Arrow gives direction, length represents the speed (use a dot for zero speed) • (net) force required to change velocity • Example: car speeding up to left 20

Free-Fall Acceleration • a = 9. 8 m/s/s in downward direction • Ex. Speed of object dropped from rest after 1. 0, 2. 0, 3. 0 seconds: • v = vo + at • v(1. 0 s) = 0 + (-9. 8)(1. 0) = -9. 8 m/s • v(2. 0 s) = 0 + (-9. 8)(2. 0) = -19. 6 m/s • v(3. 0 s) = 0 + (-9. 8)(3. 0) = -29. 4 m/s / 21

Activities • Moving Man phet animae • Textbook type problems 22

Summary: • • speed: rate of travel average speed: distance traveled/time. displacement: change in position velocity: rate position changes acceleration: rate velocity changes kinematic equation set free fall: constant acceleration. graphs and slopes 23