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 2-1Position, Distance, and Displacement 2-2Average Speed and Velocity 2-3Instantaneous Velocity 2-4Acceleration 2-5Motion with Constant Acceleration 2-6Applications of the Equations of Motion 2-7Freely 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 2-2 One-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?

Conceptual Checkpoint 2-1 Average Speed The AVERAGE SPEED is the total distance traveled, divided by the total time of travel. We’ll do this “by the numbers”, but first, let’s see what your instincts tell you.

What is the average speed? 1.Greater than 40 mph. 2.Less than 40 mph. 3.Equal to 40 mph.

What is the average speed? 1.Greater than 40 mph. 2.Less than 40 mph. 3.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.

Example 2-2 Sprint Training Compare the average speed, and average velocity.

Figure 2-4 Motion Along the X Axis Represented with an x-Versus-t Graph

Figure 2-5a Average Velocity on an x-Versus-t Graph

Figure 2-6 Constant Velocity on an x-Versus-t Graph

Figure 2-7 Instantaneous Velocity

Figure 2-8 Graphical 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 2-9 v-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 2-10 Graphical Interpretation of Average and Instantaneous Acceleration

Example 2-3 An Accelerating Train

Cars Accelerating or Decelerating which picture matches which graph?

Figure 2-13a The Average Velocity Definition: change in velocity divided by time. Special case: Constant acceleration

Example 2-6 Put the Pedal to the Metal

Figure 2-16 Velocity 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 2-9a Catching a Speeder Q: How many mph?

Table 2-4 Constant-Acceleration Equations of Motion Variables RelatedEquationNumber Velocity, time, acceleration v = v 0 + at2-7 Initial, final, and average velocity v av = ½(v 0 + v)2-9 Position, time, velocity x = x 0 + ½(v 0 + v)t2-10 Position, time, acceleration x = x 0 + v 0 t + ½ at Velocity, position, acceleration v 2 = v a(x – x 0 ) = v a  x 2-12

Figure 2-22 Problem 2-3

Figure 2-25 Problem 2-17

Figure 2-26 Problem 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 2-28 Problem 2-32 What is the average acceleration for each segment, what is the average acceleration for the whole motorcycle ride?

Figure 2-29 Problem 2-33 CAREFUL! What is the displacement for each segment of the graph shown? Problem solving: 1.Draw a picture (given) 2.What are they asking for? 3.What is given? 4.What are the mathematical relationships?