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Motion

Motion. Hewitt, Ch. 2. Distance. The space between two points Easy to measure in a classroom Harder outside Lasers (chains) Sextants Straight line?. Great Circle Routes and Rhumb Lines. Great Circle Route: The shortest distance between any two points on Earth. Rhumb Line:

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Motion

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  1. Motion Hewitt, Ch. 2

  2. Distance • The space between two points • Easy to measure in a classroom • Harder outside • Lasers (chains) • Sextants • Straight line?

  3. Great Circle Routes and Rhumb Lines Great Circle Route: The shortest distance between any two points on Earth. Rhumb Line: Lines of constant direction and facilitate plotting directions between two points. From geo_tools1 GPH 111

  4. Average Speed • What is it? • Total distance traveled per unit of time. • If you did 55 miles in one hour, how fast do you think you were going in mph? • 55 mph or miles per hour, or m/hr

  5. The Formula • Note: this formula does not take into account variations due to differences in speed during any point during its travel.

  6. Units • English: • Miles, yards, feet, inches • Metric: • Kilometers, meters, centimeters, millimeters • Since speed is measured as distance per unit of time, speed can be represented as: • Miles/hour, kilometers/hour, feet/second, meters/second

  7. Instantaneous Speed • Instantaneous speed is the speed of an object at any instant in time. • Ex. The speedometer in your car.

  8. Measuring Speed • Distance versus time • Person walking • m/sec • Mi/hr • Bowling balls rolling • People Running

  9. Running the 100m Race • How do you think the runner’s speed changes during the race? • 2007 World Championships 100m Final - Osaka, Japan • What does the runner’s speed start at? • What happens during the early part of the race? • What happens during the latter part of the race?

  10. Running the 200m race • How would you run the 200 meter race compared to the 100 meter race? • 2007 World Championships 200 m Final - Osaka, Japan • - Usain Bolt 200m race

  11. Running the 1500 m race • How do you think the runner’s speed differs compared to that of the sprinter who runs 100m? • 2007 World Championships 1500 meter Run - Osaka, Japan • Men’s 1500m run 2014 Thorpe Cup

  12. Example #1 • Calculate the average speeds of women who hold Penn Relays records in the 100, 200, 400, and 1500 m runs. What is the pattern of speeds? • Remember: v = d/t • At 100 meters: v = (100 m)/(11.44 s) = 8.74 m/s • At 200 meters: v = (200 m)/(23.66 s) = 8.45 m/s • At 400 meters: v = (400 m)/(52.33 s) = 7.64 m/s • At 1500 meters: v = (1500 m)/(264 s) = 5.68 m/s • Note that as the distance increases, the speed decreases.

  13. Example #2 • How do the amounts of time taken to travel the first and last 50 meters of the race differ for a World Class Sprinter? • It took 5.61 seconds to run the first half (50 meters) of the race. By subtraction, it took only 4.25 seconds to run the second half of the race. Therefore, it took 1.26 seconds less to run the second half of the race!

  14. Mnemonic d v t

  15. Examples • If I am running at 10m/sec, how far do I go in 10 sec? 1 minute? • If I go 2km in 30 minutes, how fast am I going? • How long does it take me to • go 100m at 5m/sec? d v t

  16. Examples • If I am driving at 50 mph, how far do I go in 1 hour? 30 minutes? • If I go 10 miles in 15 minutes, how fast am I going? • How long does it take me to • go 100 mi at 20 mph? d v t

  17. Examples • How far can I go in an hour if I am traveling at 55 mph? • 2) How far can I go if I travel at 50mph for 30 minutes? • 3) How far can I go if I travel 30 minutes at 50mph and 30 minutes at 30mph? • 4) What is my average speed for this trip? (v = d/t) • 5) If it takes 2 seconds for the sound of a gunshot to reach me, and the gun is fired from 1115 feet away, how fast is the speed of sound • a) In feet per second? • b) In miles per hour?

  18. P T graphs What does a car speeding up at constant speed look like? What does a bowling ball rolling down a ramp look like? What does a car gently braking look like? What does a car slamming on the brakes look like?

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