Chapter 2 -Section 1 1-Dimensional Kinematics

1. Chapter 2-Section 11-Dimensional Kinematics The motion of automobiles, Hot Wheel cars, and rockets are used to illustrate the physics of position, velocity, acceleration, and kinematic graphing.

2. Kinematics Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.

3. Motion • Motion happens all around us. • One – dimensional motion is the simplest form of motion. • The object can only move in one dimension • forward and backward • left and right • up and down

4. Motion • Motion takes place over time and depends on a frame of reference. • Frame of Reference – a coordinate system for specifying the precise location of objects in space • The choice of a reference point is arbitrary, but once chosen, the same point must be used throughout the problem.

5. Distance and Displacement • Distance and displacement are two quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions. • Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. • Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

6. Distance and Displacement To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. Distance traveled = Displacement = 12 m 0 m

7. Distance and Displacement The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D. Use the diagram to determine the distance traveled by the skier and the resulting displacement during these three minutes. Distance traveled = Displacement = 420 m 140 m

8. Seymour Butz views football games from under the bleachers. He frequently paces back and forth to get the best view. The diagram below shows several of Seymour's positions at various times. At each marked position, Seymour makes a "U-turn" and moves in the opposite direction. In other words, Seymour moves from position A to B to C to D. What is Seymour's resulting displacement and distance of travel? Distance = 95 yards Displacement = 55yards

9. Displacement Δx = xf – xi Displacement = change in position Displacement = final position – initial position

10. Speed and Velocity • Speed is a scalar quantity which refers to "how fast an object is moving.“ • Velocity is a vector quantity which refers to "the rate at which an object changes its position."

11. Speeding Little Old Lady Sorry, Ma’am, but you were doing 45 mph in a 30 mph zone. But I haven’t driven 45 miles yet. Okay, okay, would you believe that I haven’t been driving for an hour yet?

12. Average Speed and Velocity • Average speed is the total distance traveled divided by the time interval • Average velocity is the total displacement traveled divided by the time interval during which the displacement occurred

13. While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Ave speed = distance traveled time of travel Ave speed = 440 mi 8 h Ave speed = 55 mi / h

14. Problem A car travels from city A to city B (100km). If the first half of the distance is driven at 50 km/h and the second half is driven at 100 km/h , what is the average velocity for the trip?

15. A 100 km B V = 50 km/h V = 100 km/h t = d/s t = 50 km 50 km/h t = 1 h t = d/s t = 50 km 100 km/h t = 0.5 h Ave. velocity = displacement time Ave velocity = 100 km 1.5 h 67km/h

16. Velocity • Constant Velocity – velocity is unchanging • Instantaneous Velocity – the velocity of an object at some instant (or specific point in its path) (slope)

17. Describing Motion with Position vs. Time Graphs The Meaning of Shape for a position-time Graph Homework

18. The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph. If the position-time data for such a car were graphed, the resulting graph would look like the graph at the right.

19. If the position-time data for such a car were graphed, the resulting graph would look like the graph at the right.

20. The position vs. time graphs for the two types of motion – constant velocity and changing velocity Positive constant velocity Positive changing velocity

21. The Principle of Slope for a p–t Graph The slope of the line on a position-time graph reveals useful information about the velocity of the object. It's often said, "As the slope goes, so goes the velocity." Something to remember

23. Let me test your understanding Match the slope with the velocity Positive slope Small velocity Constant slope Positive velocity Small slope Constant velocity

24. Answers : Positive slope Positive velocity Constant velocity Constant slope Small velocity Small slope

25. Comparing slopes and velocity Fast, rightward, Constant velocity Slow rightward, Constant velocity

26. Fast, leftward Constant velocity Slow , leftward Constant velocity

27. Leftward velocity, Slow to fast Leftward velocity, Fast to slow

28. The Passing Lane

29. Constant Positive Velocity

30. Constant Negative Velocity