1 2 Kinematics distance, location, displacement speed, velocity, acceleration free fall Homework: 7, 8, 11, 31, 33, 41, 45, 65, 70, 88, 100, 101.

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

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

Initial/Final Notation 4 Same rules apply for all variables

Delta Notation 5 called Displacement

6 Velocity (m/s) When  t is small,  x/  t is the instantaneous velocity v.

7 Acceleration (m/s/s) If  t is small,  v/  t is called the instantaneous acceleration and labeled “a”.

Ex. Car Acceleration 8 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 9

Average Velocity with Uniform Acceleration Uniform Acceleration = constant valued acceleration During uniform acceleration, average velocity is halfway between vo and v: 10

Average Velocity Formula 11

Displacement Formula 12

V-squared Equation 13

14 Kinematic Equations with Constant Acceleration

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

16 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 60mph = 27m/s, what is the skid-to-stop distance on a wet road?

17 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.

18 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

19 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 20

21 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 (p.46) free fall: constant acceleration. graphs and slopes