Chapter 2 Motion Along a Straight Line Figure 2.5 Describing Motion Interested in two key ideas: How objects move as a function of time • Kinematics • Chapters 2 and 3 Why objects move the way they do • Dynamics • Do this in Chapter 4 and later Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Table 2.2 Chapter 2: Motion in 1-Dimension Velocity & Acceleration • Equations of Motion • Definitions • Some calculus (derivatives) • Understanding displacement, velocity curves • Strategies to solve kinematics problems • Motion with constant acceleration – Free falling objects Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Equations of Motion We want Equations that describe: Where am I as a function of time? How fast am I moving as a function of time? What direction am I moving as a function of time? Is my velocity changing? Etc. Where will I land? Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Motion in One Dimension Where is the car? • X=0 feet at t =0 sec 0 • X=22 feet at t =1 sec 1 • X=44 feet at t =2 sec 2 We say this car has “velocity” or “Speed” Plot position vs. time. How do we get the velocity from graph? Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Motion in One Dimension Cont… Velocity: “Change in position during a certain time period” Calculate from the Slope: The “Change in position as a function of time” • Change in Vertical • Change in Horizontal Change: D Velocity  DX/Dt Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Constant Velocity Equation of Motion for this example: X = bt+x with x =0 0 0 • Slope is constant • Velocity is constant – Easy to calculate – Same everywhere Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Moving Car A harder example: X = ct2 What’s the velocity at t=1 sec? Want to calculate the “Slope” here. Instantaneous Velocity What would my speedometer read? x(t  t)  x(t) dx v(t)  lim  t0 t dt Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley