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Distance and Displacement

Distance and Displacement. Chapter 11.1. Key Concepts and Vocabulary. Key Concepts: What is needed to describe motion completely? How are distance and displacement different? How do you add displacements? Vocabulary: Frame of Reference Relative Motion Distance Vector Resultant Vector.

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Distance and Displacement

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  1. Distance and Displacement Chapter 11.1

  2. Key Concepts and Vocabulary • Key Concepts: • What is needed to describe motion completely? • How are distance and displacement different? • How do you add displacements? • Vocabulary: • Frame of Reference • Relative Motion • Distance • Vector • Resultant Vector

  3. Distance • Length of a path between two points. • Units: kilometers, meters, centimeters

  4. Displacement • Direction from the starting point and the length of a straight line from the starting point to the ending point.

  5. Displacement Along A Straight Line 20km 30km 15km 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 Displacement = 20 km + 30 km + 15 km = 65 km east -10km 30km 30km Displacement = 40 km + -10 km + 40 km = 70 km east

  6. Vector • Vectoris a quantity that has magnitude and direction • 12 km northwest • Magnitude – size, length, or amount • Length of arrows shows the magnitude

  7. Vector Addition Problems

  8. Displacement That Isn’t Along a Straight Line • When two or more displacement vectors have different directions, they can be combined by graphing.

  9. Based on the red arrows, how far did Mrs. Ewald walk? Add the magnitudes of each vector along the path. 2 long blocks south 2 short blocks east 1 long block south 3 short blocks east Total = 8 blocks or 11 short blocks Path walked by Mrs. Ewald 1 long block = 2 short blocks

  10. Based on the red arrows, how far did Mrs. Ewald walk? • The vector in yellow is the resultant vector – vector sum of two or more vectors. • Points directly from start to finish. Resultant vector = 8 short blocks Path walked by Mrs. Ewald

  11. Question? • Mrs. Ewald walks 4m east, 2m south, 4m west, and 2m north. • What is the total distance Mrs. Ewald walked? • What is the total displacement? 4m + 2m + 4m + 2m = 12m Displacement = 0m 4m 2m 2m 4m

  12. Speed andVelocity Chapter 11.2

  13. Key Concepts and Vocabulary • Key Concepts: • How is instant speed and average speed different? • How are speed and velocity different? • Vocabulary: • Speed • Average Speed • Instantaneous Speed • Velocity

  14. Speed • Ratio of the distance an object moves to the amount of time the object moves. • Equations:

  15. Velocity • The speed and direction an object is moving relative to a reference point. • Equations:

  16. Example • A car travels 85 km from Town A to Town B, then 45 km from Town B to Town C. The total trip took 1.5 hours. What was the average speed of the car?

  17. Example • A bicyclist travels for 1.5 hours at an average speed of 32 km/h. How far does the bicyclist travel in that time?

  18. Example • A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometers in 16 minutes. What is the joggers average speed in kilometers per minute?

  19. Example • A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed?

  20. Acceleration Chapter 11.3

  21. Key Concepts and Vocabulary • Key Concepts: • How are changes in velocities described? • How can you calculate acceleration? • Vocabulary: • Acceleration • Free Fall

  22. Acceleration • A vector described as a changes in speed, changes in direction, or changes in both. • Change in Speed • Free fall (9.8 m/s2) • Change in Direction • Riding a merry-go-round • Changes in Speed and Direction • Speeding up around a corner

  23. Calculating Acceleration • Equation: Acceleration = Change in Velocity Time Acceleration = Velocityfinal – Velocityinitial Time a = vf – vi t • Unit of Measure: m/s2, km/s2

  24. Example • A car travelling at 10 m/s starts to slow down steadily. It comes to a complete stop in 20 seconds. What is its acceleration?

  25. Example • An airplane travels down a runway for 4.0 seconds, with an acceleration of 9.0 m/s2. What is its change in velocity during this time?

  26. Example • A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water?

  27. Example • A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boys hand?

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