1. Motion in One Dimension Mechanics – study of the motion of objects and the related concepts of force and energy. Dynamics – deals with why objects move as they do. Kinematics – description of how objects move.

2. Measurement of Motion Scalar – physical quantity that only involves magnitude and units. Vector – physical quantity that has magnitude and direction. Indicated by boldface line and arrow (  )

3. KEYWORDS- look them up! ACCELERATION DISPLACEMENT DISTANCE

4. KEYWORDS VELOCITY SPEED FREE FALL

5. Frame of Reference A position from which an observation or measurement is made.

6. Coordinate axes Graph that represents the “frame of reference”. x and y axis. origin indicated by (0,0). (+) and (–) positions on x and y axis indicate direction.

7. Displacement Change in the position of an object. Distance is magnitude only (scalar quantity). Displacement is a vector quantity represented by  x. (magnitude and direction) SI Unit: meter

8. Scalar vs. Vector Scalar –magnitude but no direction. Vector –physical quantity that has both direction and magnitude.

9. Displacement (cont.) The sign of displacement indicates the direction. Positive (+) = object moving to the right on the x axis. Negative (-) = object moving to the left on the x axis.

10. Speed How fast an object travels in a given time interval (differs from velocity). Speed is a scalar quantity represented by v s. SI Unit: m/s v s =  d  t

11. Velocity Signifies –magnitude of how fast an object is moving (numerical value) –direction in which it is moving. Velocity is a vector quantity represented by v. (has magnitude and direction) SI Unit: m/s with the direction of displacement

12. Velocity (cont.) average velocity v avg =  x  t –Velocity can be positive or negative –speed is never negative Instantaneous Velocity – velocity at one point in time.

13. Graphing of Velocity Position vs. time Graph x-axis: time in seconds y-axis: displacement in meters Slope =  d which is the velocity  t If the graph is linear –constant velocity If the graph is not linear –changing velocity (accelerating or decelerating)

14. Acceleration Rate of change of velocity Acceleration is a vector quantity represented by a. SI Unit: m/s 2 including the direction. Average acceleration a =  v  t

15. Acceleration (cont.) Instantaneous acceleration –acceleration at a given point in time. –Shown by drawing a line tangent to the point on the curve. –Then calculate the slope of the tangent line.

16. Graphing Acceleration Velocity vs. time graph x-axis: time in seconds y-axis: velocity in m/s Slope = acceleration Direction and Magnitude of acceleration can be seen in a graph.

17. Alternative Formulas for calculating variables related to velocity and acceleration The 4 equations derived for one- dimensional motion when acceleration is constant: v f = v i + a  t v f 2 = v i 2 + 2a  x  x = 1/2(v i + v f )  t  x = v i  t +  1/2 a (  t) 2

18. Free Fall All objects dropped near the surface of a planet, in the absence of air resistance, fall with the same constant acceleration. The constant acceleration is due to the pull of gravity.

19. Free Fall (cont.) Since downward direction isarbitrarily considered a negative value, acceleration of objects in free fall is negative. g = - 9.81 m/s 2

20. Free Fall Acceleration is always negative It is negative in an upward direction because the object is slowing down. It is negative in a downward direction because by convention, downward is indicated by a negative sign.

21. Sample Problem 1 During a race on level ground, Andrea covers 825 m in 137 s while running due west. Find Andrea’s average velocity.

22. Sample Problem 2 Eugene is 75 km due south of Salem. If Joe rides from Salem to Eugene on his bike in 6 h, what is his average velocity?

23. Sample Problem 3 Simpson drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway?

24. Sample Problem 4 As a shuttle bus comes to a normal stop, it slows from 9 m/s to 0 m/s in 5s. Find the average acceleration of the bus.

25. Sample Problem 5 With an average acceleration of - 0.5 m/s 2, how long will it take a cyclist to bring a bicycle with an initial velocity of 13.5 m/s to a complete stop?

26. Sample Problem 6 A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8 m/s 2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

27. Sample Problem 7 Jason hits a volleyball so that it moves with an initial velocity of 6 m/s straight upward. If the volleyball starts from 2m above the floor, how long will it be in the air before it strikes the floor?