Chapter 2: Motion Along a Line Position & Displacement Speed & Velocity Acceleration Describing motion in 1D Free Fall CQ: 1, 2, 3, 4. P:1, 11, 13, 25, 27, 29, 47, 50.

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

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

Initial/Final Notation Same rules apply for all variables

Delta Notation called Displacement

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

Graphs Wilson (12) x vs t Giambattist (21) +, -, 0 accel.

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

Ex. Car Acceleration from 10m/s to 15m/s in a time of 2.0 seconds. from 10m/s to 15m/s in a time of 2.0 seconds. In this class we only use average acceleration and often drop the “avg” notation from acceleration.

Velocity Formula

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:

Average Velocity Formula

Displacement Formula

V-squared Equation

Kinematic Equations with Constant Acceleration

Ex. Human Acceleration In the 1988 Olympics, Carl Lewis reached the 20m mark in 2.96s (Bolt: 2.87s)

Ex: V2 Equation Approximate Stopping Accelerations in m/s/s: Approximate Stopping Accelerations in m/s/s: Dry Road: ~ 9 (anti-lock) ~ 7 (skidding) Wet Road: ~ 4 (anti-lock) ~ 2 (skidding) At 60mph = 27m/s, what is the skid-to-stop distance on a wet road?

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.

Motion Diagrams Are velocity-position 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

Free-Fall Acceleration a = 9.8m/s/s in downward direction Ex. Speed of object dropped from rest after 1.0, 2.0, 3.0 seconds: v = vo + at v(1.0s) = 0 + (-9.8)(1.0) = -9.8m/s v(2.0s) = 0 + (-9.8)(2.0) = -19.6m/s v(3.0s) = 0 + (-9.8)(3.0) = -29.4m/s /

Activities Moving Man phet animae Textbook type problems

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