Review and Announcements • Tatiana Brusentsova is the Teaching Assistant/Grader. • My office hours will take place in Room 402 of the Physics Department. • Make sure you are using WebAssign by the end of the week! Homework #1 due Monday.
Chapter 2: One-Dimensional Kinematics • Outline • 2-1 Position, Distance, and Displacement • 2-2 Average Speed and Velocity • 2-3 Instantaneous Velocity • 2-4 Acceleration • 2-5 Motion with Constant Acceleration • 2-6 Applications of the Equations of Motion • 2-7 Freely Falling Objects
Major Concepts • Position, distance and displacement • Speed and velocity • Average • Instantaneous • Constant • Acceleration • Average • Instantaneous • Constant • Graphs of position versus time, velocity versus time, and acceleration versus time • Equations of motion with constant acceleration • Free fall Warning Areas: Speed vs. Velocity Distance vs. Displacement Constant Velocity vs. Constant Acceleration
Distance and displacement • Displacement is the net change in position from beginning to end of a journey • Distance is the total amount of change in position, including re-tracing your steps on the journey. Physics uses common terms in technical ways.
Figure 2-2One-Dimensional Coordinates Try some examples…
Speed and Velocity • Speed is the distance traveled in a period of time. It is a “scalar” (number only). • Velocity is the displacement in a period of time. It is a “vector” (number and direction).
Distance and displacement What is the displacement at 1s, 2s, 3s, 4s? What is the distance traveled at 1, 2, 3, 4s?
What is the average speed? • Greater than 40 mph. • Less than 40 mph. • Equal to 40 mph. Cross-Tab Label 0 / 100
What is the average speed? • Greater than 40 mph. • Less than 40 mph. • Equal to 40 mph. Problem solving: -draw a picture -label all quantities -identify “unknown” -write down relationships (formulas), working backwards from unkown to known -find a formula for the unknown -plug in the numbers Etc. Cross-Tab Label 0 / 100
Example 2-2Sprint Training Compare the average speed, and average velocity.
Figure 2-4Motion Along the X Axis Represented with an x-Versus-tGraph
Figure 2-8Graphical Interpretation of Average and Instantaneous Velocity
Our first formula! If the velocity is constant, then the average velocity is the same as the instantaneous velocity. Rearranging:
Acceleration • Acceleration is the change in velocity per unit time • The average acceleration is the change in velocity per change in time. It is a vector quantity.
Figure 2-9v-Versus-t Plots for Motion with Constant Acceleration
Our second formula! For constant acceleration… Velocity versus time produces a straight line graph, if acceleration is constant.
Figure 2-10Graphical Interpretation of Average and Instantaneous Acceleration
Cars Accelerating or Deceleratingwhich picture matches which graph? 1 2 3 4
Figure 2-13aThe Average Velocity Special case: Constant acceleration Definition: change in velocity divided by time.
Figure 2-16Velocity as a Function of Position for the Ranger in Example 2-8 Notice that ½ the speed is lost in last ¼ of stopping distance. CONSTANT DECELERATION
Example 2-9aCatching a Speeder Q: How many mph?
Figure 2-26Problem 2-21 Find the average velocity for each segment of the “walk”, and for the total “walk”. Now, compare DISPLACEMENT and DISTANCE. Compare, average VELOCITY and SPEED.
Figure 2-28Problem 2-32 What is the average acceleration for each segment, what is the average acceleration for the whole motorcycle ride?
Figure 2-29Problem 2-33 CAREFUL! What is the displacement for each segment of the graph shown? • Problem solving: • Draw a picture (given) • What are they asking for? • What is given? • What are the mathematical relationships?