Physics 1 – Sept 8, 2016 Get out 2.1 p1-2 Worksheet for Homework Check. P3 Challenge – Do Now (on slips of paper) True/False: 1) Distance is a vector quantity and displacement is a scalar quantity. 2) A person makes a round-trip journey, finishing where she started. The displacement for the trip is 0 and the distance is some nonzero value. 3) A person starts at position A and finishes at position B. The distance for the trip is the length of the segment measured from A to B. 4) If a person walks in a straight line and never changes direction, then the distance and the displacement will have exactly the same magnitude. 5) The phrase "20 mi, northwest" likely describes the distance for a motion. 6) The phrase "20 m, west" likely describes the displacement for a motion.

Objectives and Agenda IB 2.1 Motion Agenda for IB 2.1 Motion 1D Motion (acceleration = 0) Agenda for IB 2.1 Motion X vs t graphs V vs t graphs Constant acceleration problems (time permitting) Assignment: IB 2.1 1D Motion Practice Worksheet p 3-5, 6?

Instantaneous Velocity and Average Acceleration Consider an ever smaller time interval: lim⁡ 𝒗 = ∆𝑠 ∆𝑡 When the time interval vanishes, the velocity you have is the instantaneous velocity. Your speedometer in a car measures instantaneous velocity from moment to moment. If the instantaneous velocity changes, then there has been some acceleration. Average acceleration is the ratio of the change in instantaneous velocity to the total time for the change to occur. 𝒂 = ∆𝒗 ∆𝑡

About Acceleration Acceleration is a vector. A positive acceleration (in the + direction) is the result of An object moving in the + direction, speeding up. OR an object moving in the – direction slowing down. A negative acceleration ( in the – direction) is the result of An object moving in the + direction, slowing down. OR an object moving in the – direction, speeding up. A larger acceleration is a large change in velocity of a given t. A larger acceleration is the same change in velocity over a shorter time.

X vs t graphs We can graph position versus time to describe the motion Graph for being at rest at the origin. Graph for being at rest at some other position. Graph for moving forward, +x direction Graph for moving backward, -x direction Graph for moving at a high velocity Graph for moving at a low velocity Graph for positive acceleration, both varieties Graph for negative acceleration, both varieties Graph for an object turning around

V vs t graphs We can also graph velocity versus time to describe the motion Velocity is the slope of the x vs t graph Graph for being at rest at the origin. Graph for being at rest at some other position. Graph for moving forward, +x direction Graph for moving backward, -x direction Graph for moving at a high velocity Graph for moving at a low velocity Graph for positive acceleration, both varieties Graph for negative acceleration, both varieties Graph for an object turning around

Constant acceleration Many types of motion occur with constant acceleration. 5 variables are used to completely describe 1D constant acceleration: s, displacement, m u, initial velocity, m/s v, final velocity, m/s a, acceleration, m/s2 t, time, s Set of 5 kinematic equations that express how these variables are related to one another. Each equation uses only 4 out of the 5 variables.

The Kinematic Equations 𝑣=𝑢+𝑎𝑡 missing s 𝑠=𝑢𝑡+ 1 2 𝑎 𝑡 2 missing v 𝑣 2 = 𝑢 2 +2𝑎𝑠 missing t 𝑠= 𝑣 𝑡= 1 2 𝑣+𝑢 𝑡 missing a 𝑠=𝑣𝑡− 1 2 𝑎 𝑡 2 missing u Things to notice: First is the definition of acceleration rearranged (Calculus: second is the first integrated) Third is what you get when you eliminate t from one and two. Fourth: For constant acceleration, average velocity is the simple average of the initial and final velocities. Fifth: Rarely used. Not even listed sometimes.

Solving Constant Acceleration Problems 1) List the five variables involved. 2) Reread the problem to identify values for 3 of the 5 variables. 3) Identify which variable is asked for and label with “?” 4) Identify the fifth variable as missing from the problem. 5) Select the kinematics equation to use. (Based on missing variable) 6) Substitute values into the equation. 7) Solve for the unknown. 8) Evaluate the answer. (Does it make sense? Sigfigs? Units?)

Sample problem A train moving in a straight line with an initial velocity of 0.50 m/s accelerates at 2.0 m/s2 for 2.0 seconds. a) What is the final velocity of the train? b) How far did the train travel during this acceleration?

Practice You are driving through town at 12.0 m/s when suddenly a basketball rolls out in front of you. You apply the brakes and begin decelerating at 3.5 m/s2 . a) How far do you travel before stopping? b) when you have traveled only half the distance in part a), what is your speed?

Exit Slip - Assignment 1) Draw a x vs t graph for an object that starts at the origin, moves quickly in the positive direction, stops for a time, then moves more slowly back to its original position. 2) Draw the corresponding v vs t graph for this motion. What’s Due on Thurs Sept 8? (Pending assignments to complete.) IB 2.1 1D Motion Practice Worksheet p 3-5, 6? What’s Next? (How to prepare for the next day) Study IB 2.1 (1 D) p35-37