Motion in One Dimension

1. Motion in One Dimension

2. Mechanics Kinematics Dynamics Describes motion. The forces that cause motion.

3. Scalars and Vectors There are two kinds of measurement: scalarsand vectors. Scalar – has only magnitude (size), such as distance. Ex. 35 m Vector– has both magnitude and direction, such as position. Ex. 45 km north

5. A jet airplane travelled at 200km/hr towards the southwest. This is an example of a • Vector • Scalar

6. 200km/hr to the southwest represents … • Speed • Velocity • Distance • Acceleration • Displacement

7. Motion Anytime an object changes its position (x), it is engaged in motion. Displacement (Δx) = change in position . Δx = xf - xi xf= final position xi = initial position

8. Reference Point Reference point (or frame of reference) – a point that you label as zero and measure objects distance from

9. Position Position (x) – the separation between an object and a reference point. - it can be positive or negative depending on which side of the reference point that it is

10. Distance vs. Displacement Joe Adams - punt return Distance (d) = total amount travelled regardless of direction (the real amount that Adams ran); scalar Displacement (Δx) = the difference between the final and initial position (the yardage that shows up in the box score); vector

11. Average Velocity

12. Average Velocity Average velocity = change in displacement per unit time __ v = (xf–xi)/ (tf–ti) =Δx/Δt = Δx/t xf= position at clock reading t2 xi= pos. at earlier clock reading t1 ∆x = xf– xi ∆t = t2 – t1

13. London Olympics and Average Velocity Pure Speed Usain Bolt and Average Velocity In the water ...

14. Is Usain Bolt’s average velocity in the 200m greater, less, or the same as in the 100m? • Greater in the 200m • Less in the 200m • The same in the 200m (+/- 1m/s)

15. Usain Bolt in the 200m

16. True or False: A car clocked with an average velocity of 85mph east must have been moving faster than a car clocked with an average velocity of 75mph east throughout the entire time interval. • True • False

17. It is possible to have a negative velocity. • True • False

18. Acceleration Acceleration – a vector quantity that describes the change in velocity over time a = Δv/t SI unit = m/s2

19. Position vs. Time Graphs Slope = velocity Straight line (constant slope) = constant velocity Curved line = changing velocity = acceleration

20. Velocity-Time Graphs Area underneath curve or line = distance traveled Constant Slope ≠0 : constant acceleration Zero slope = constant velocity

21. Acceleration Time Graphs Used to visually show changes in acceleration. Area under line = velocity

22. The marble will finish first at the end of which color ramp? (Let the betting begin.) • Red • Green • Yellow • Blue • All the same

23. The marble will complete the race with the least time on which color ramp? • Red • Green • Yellow • Blue • All the same

24. Which ramp will the marble have the fastest average velocity? (Place your bets.) • Red • Green • Yellow • Blue • All the same

25. Which color ramp will the marble have the smallest instantaneous velocity at the end of the ramp? (Place your bets.) • Red • Green • Yellow • Blue • All the same

26. Which color ramp will the marble have the largest instantaneous velocity at the end of the ramp? (Place your bets.) • Red • Green • Yellow • Blue • All the same

27. Types of Velocity Constant velocity – this is a situation where the average velocity is the same for all time intervals. Average velocity – takes into account the entire displacement and time; velocity may not always be constant Instantaneous velocity – velocity at a given instant

28. Acceleration Acceleration – a vector quantity that describes the change in velocity over time a = Δv/t = (vf – vi)/t SI unit = m/s2

29. Acceleration A rocket ship has a negative acceleration but still seems to be speeding up. Is this possible? Justify your answer with concrete details backed up by data.

30. Acceleration Matrix

31. A car speeds up from 10 m/s south to 30 m/s south. Describe the acceleration. • Positive • Negative • Zero • Unable to be determined

32. A cheetah slows down from 10 m/s south to 5 m/s south. Describe the acceleration. • Positive • Negative • Zero • Unable to be determined

33. A minivan slows down from 85 mi/hr to 65 mi/hr when the driver spots a police officer tracking her speed. Describe her acceleration. • Positive • Negative • Zero • Unable to be determined

34. An basketball is released from rest. When the ball hits the ground it is moving at a speed of 8m/s. Describe the acceleration. • Positive • Negative • Zero • Unable to be determined

35. Tips for Solving Physics Problems • 1) List all given information including unknown variable. • Look for any inconsistent units (ex. cm and m/s) • If all values are in SI units to start with, the final value will be an SI unit. • 2) List formulas that will be used to solve the problem (before plugging in data). • 3) Plug in data and solve for unknown. • 4) Box your answer and make sure the correct unit is present

36. Δx t vf vi a Equations of Motion at Constant Acceleration