1. Chapter 2. Motion in One Dimension

2. Terminology Mechanics Mechanics : Study of objects in motion. Kinematics :HOW Kinematics : Description of HOW objects move. (Chapters 2 & 4) WHY No reference to WHY objects move. Dynamics : Dynamics : WHY objects move. FORCE!!! Introduction of the concept of FORCE!!! (Most of the course after Chapter 5)

3. Terminology, cont Translational Motion: Translational Motion: Motion with no rotation. Rectilinear Motion: Rectilinear Motion: Motion in a straight line path. Particle Model (Moving Object): Particle Model (Moving Object): Point-like object. An object with mass and neglected size.

4. Vectors and Scalars Vector quantities magnitude direction Vector quantities need both magnitude (size or numerical value) and direction to completely describe them. +– Will use + and – signs to indicate vector directions Scalar quantities magnitude Scalar quantities are completely described by magnitude only!!

5. 2.1 Position, Velocity, Speed frame of reference Defined in terms of a frame of reference x- or y- axis One dimensional, so generally the x- or y- axis object’s position The object’s position is its location with respect to the frame of reference

6. Active Figure 2.1 (SLIDESHOW MODE ONLY)

7. Position-Time Graph The position-time graph shows the motion of the particle (car) The smooth curve is a guess as to what happened between the data points

8. Displacement Displacement vector: Displacement (vector): change in position during some time interval Represented as (2.1) SI units(m)  x SI units are meters (m)  x can be positive or negative Distance≠ Displacement Distance traveled by the object ≠ Displacement of the object!!!

9. Average Velocity average velocityvector The average velocity (vector): rate at which the displacement occurs (2.2) (2.2) The dimensions[L/T] The dimensions are length / time [L/T] SI units(m/s) SI units are (m/s) the slope Is also the slope of the line in the position-vs-time graph

10. Average Speed Average Speed Average Speed is a scalar quantity same units as velocity(2.3) The average speed is NOT (necessarily) the magnitude of the average velocity!!!! The average speed is NOT (necessarily) the magnitude of the average velocity!!!!

11. Example 2.1Displacement Example 2.1 Displacement x 1 = 30 m x 2 = 10 m x 1 = 30 m x 2 = 10 m Displacement VECTOR Displacement is a VECTOR

12. Example 2.2Average Velocity & Speed Example 2.2 Average Velocity & Speed Suppose the person walks during 50 seconds. Displacement Displacement Distance (d) = 100m Average velocity: Average velocity: Average Speed: Average Speed: XfXf XiXi

13. 2.2 Instantaneous Velocity and Speed Instantaneous Velocity  Limit of the average velocity Instantaneous Velocity  Limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero instantaneous velocity The instantaneous velocity indicates what is happening at every point of time

14. Instantaneous Velocity (Velocity) instantaneous velocity The general equation for instantaneous velocity is(2.4-2.5) positive, negative, or zero The instantaneous velocity can be positive, negative, or zero

15. Instantaneous Velocity, graph The instantaneous velocityslope x t The instantaneous velocity is the slope of the line tangent to the x vs t curve green This would be the green line blueaverage velocity green The blue lines (average velocity) show that as  t gets smaller, they approach the green line

16. Instantaneous Speed (Speed) The instantaneous speed the magnitudeinstantaneous velocity The instantaneous speed is the magnitude of the instantaneous velocity average speed NOTaverage velocity Remember: the average speed is NOT the magnitude of the average velocity

17. uniform velocity (constant),Instantaneous velocity average velocity If an objects moves at uniform velocity (constant), then: Instantaneous velocity and average velocity at any instant (t) are the same. Instantaneous = average Example 2.3Instantaneous & average velocities Example 2.3 Instantaneous & average velocities

18. Instantaneous velocity Average velocity NOT ALWAYS!!!! Are Instantaneous velocity and Average velocity at any instant t the same? NOT ALWAYS!!!! Example: Example: A car starts from rest, speed up to 50km/h, remains at that speed for a time. Slow down to 20 km/hr in a traffic jam, the finally stops. Traveling a total of 15 km in 30 min (0.5 hr). Similar to Question #4 Homework!!! Similar to Question #4 Homework!!! Example 2.4Instantaneous & average velocities Example 2.4 Instantaneous & average velocities

19. Example 2.4 Instantaneous & average velocities, cont

20. Examples to Read!!! Examples to Read!!! Example 2.2 Example 2.2(Page 30) Example 2.3 Example 2.3(Page 30) Homework Problems to be solved in Class!!! Homework Problems to be solved in Class!!! Problem: 3 Problem: 3 Problem: 6 Problem: 6 Material for the Midterm