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Motion In One Dimension

Motion In One Dimension. One dimensional motion. Motion in a straight line. No left or right motion Example: Train traveling down straight track. Frame of reference. How fast is your desk moving? RELATIVE TO THE FLOOR – AT REST RELATIVE TO THE SUN – 30km/s

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Motion In One Dimension

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  1. Motion In One Dimension

  2. One dimensional motion • Motion in a straight line. • No left or right motion • Example: Train traveling down straight track

  3. Frame of reference • How fast is your desk moving? • RELATIVE TO THE FLOOR – AT REST • RELATIVE TO THE SUN – 30km/s • Definition: Coordinate system for specifying the precise location of objects in space.

  4. Any frame of reference can be chosen, but must be consistent • Some make explaining easier

  5. Displacement • Change in position or Δx =xf – xi

  6. What is the gecko’s displacement? x = xf – xi Remember: Delta represents “change” • Displacement of Gecko Δx= 85cm – 22cm = 63cm

  7. What is the gecko’s displacement if he climbed a tree? UP 60cm DOWN 30cm Δy = yf – yiΔy = 60cm – 30cm30cm upward

  8. UP 60cm DOWN 30cm Displacement is NOT always distance traveled What is the distance traveled by the gecko? 90cm

  9. UP 60cm DOWN 30cm BUT, displacement… y = 60cm – 30cm30cm up

  10. What would the gecko’s displacement have been if he returned to the 20cm mark? Zero Displacement

  11. Displacement describes direction Positive = right Negative = left

  12. B d = 20 m A Distance and Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: Distanced is a scalar quantity (no direction): Contains magnitude only and consists of a number and a unit. (20 m, 40 mi/h, 10 gal)

  13. x = 12 m, 20o B A q Distance and Displacement Displacement is the change in position. Must include magnitude and direction. A vector quantity: Contains magnitude AND direction. (12 m, 300; 8 km/h, N)

  14. B A Distance vs Displacement • Draw the distance and displacement of a particle that moves from A to B around an oval track.

  15. B A Distance vs Displacement

  16. Speed • How fast something is moving • Rate at which distance is covered • Distance covered per unit of time • Ex: km/s mi/h Remember: Rate is a clue that something is being divided by time.

  17. Velocity Speed in a given DIRECTION

  18. Average Velocity • Positive or Negative • Depends of sign of the displacement • Time is always positive

  19. Tile Board Time

  20. Jessica drove 370km west (negative) on a straight highway to visit a friend. She left at 10a.m. and arrived at 3p.m. What is her average velocity? Change in displacement -370km Change in time  5.0h Average Velocity  -74 km/h Remember: This is an average. Jessica didn’t travel exactly that speed the entire trip.

  21. During a race, Jason runs with an average velocity of 6.02 m/s to the east. What displacement does Jason cover in 137s? • Ans: 825m to the east

  22. If Matt rides south on his bicycle in a straight line for 15 minutes with an average speed of 12.5 km/h, how far has he ridden? Ans: 3.1 km south

  23. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min, then it travels 210 km south with an average velocity of 75 km/h to the south.A. How long does the total trip last?Ans: A. 6.4 h

  24. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min, then it travels 210 km south with an average velocity of 75 km/h to the south.B. What is the avg. vel. for the total trip? B. 77km/h south

  25. Graphically Interpreting Velocity Remember the dropped ball experiment? Why is this line curved?

  26. Graphically Interpreting Velocity The amount of distance covered increases per unit of time (second) as time goes along 15.33 6.47

  27. slope Slope = Avg Vel Must be a straight line

  28. Positive Velocity At Rest Negative Velocity Straight Line Graphs of 3 Different Objects

  29. Instantaneous may NOT be the same as average velocity Slope of tangent line = Instantaneous velocity

  30. Tile Board Warm-UpDon’t write the question – Just show all your work A sprinter has been clocked at 9 s flat for the 100yd dash. (His coach has predicted an undefeated season.) A. How fast is he traveling in mi/h? B. Is this his final velocity? • When do you think he would attain his greatest velocity?

  31. 100yd- 0 yd 9s – 0s = 11.11yd/s Givens:x = 100ydt = 9 sec 11.11 yd 1 s 3600s 1h 3 ft 1yd 1 mi 5280ft 22.72 mi/h

  32. B. Is this his final velocity?C. When do you think he would attain his greatest velocity? B. NO, it is his average velocity. • In theory, assuming all sprinters start from rest and continue to accelerate throughout the entire race, he should attain his greatest velocity as he crosses the finish line.

  33. = 55,556mi/h2 = 48,000mi/h2 Acceleration Who has the greater acceleration: • Logan’s Mousetrap Car doing 0 to 60mi/h in 3.9s (.00108 h) B. Micah’s Mousetrap Car doing 0 to 60 mi/h in 4.5s (.00125 h) SOLUTION: Change in velocity is EQUAL: 60 mi/h Time is DIFFERENT: A. 60mi/h B. 60mi/h .00108h .00125h Logan’s The WINNER

  34. Acceleration Remember: Rate is a clue that something is being divided by time. • The RATE of change in velocity UNITS

  35. Best Accelerator of All Times Quickest to change • He could change **directions on a dime **speed quicker than anyone • OSU 1988 • 2,628 rushing yds • 39 touchdowns!! • Super thighs: Could squat 600 lbs!!!

  36. Tile Board Time

  37. Ans: 2.2s

  38. ANS: 2.0s

  39. With an average acceleration of -0.50 m/s2, how long does it take a cyclist to bring a bicycle with an initial speed of 13.5 m/s to a complete stop? ANS: 27s

  40. Suppose a treadmill has an avg accel. • of 4.7 X 10-3 m/s2. • How much does its speed change • after 5.0 min? • B.If the treadmill’s initial speed is • 1.7 m/s, what will its final speed be? A. 1.4m/s

  41. Suppose a treadmill has an avg accel. of 4.7 X 10-3 m/s2. B.If the treadmill’s initial speed is 1.7 m/s, what will its final speed be? B. 3.1 m/s

  42. Acceleration has DIRECTION AND MAGNITUDE A. Train takes off from station to the east Δv = +  accel = + C. Train slows down as it nears a town Δv = -  accel = - B. Train travels east at a constant velocity Δv=0  accel = 0

  43. What if the train would have been moving to the WEST v = neg Acceleration = neg What if the graph continued and the velocity became negative. What does this indicate about the train? Ans: Slowed to 0 mi/h Started heading WEST

  44. Runaway Train If a passenger train is traveling on a straight track with a NEGATIVE velocity and a POSITIVE acceleration, is it speeding up or slowing down? Time is increasing (positive) We aren’t “going back in time” Hey, this isn’t “Back to the Future” Slowing Down Δv=(-30mi/h)-(-50mi/h) Negative Velocity because its going to the WEST Must be a LARGER neg. So that Δv = +

  45. Vel vs. Time Graph Rise = + accelerating + Velocity = EAST vf vi Test your Understanding

  46. Vel vs. Time Graph Down = Neg acceleration - Velocity = WEST time Velocity vi vf A

  47. Vel vs. Time Graph Down=Neg accelerating + Velocity = EAST vf vi

  48. Vel vs. Time Graph RISE = + acceleration - Velocity = WEST time vf Velocity vi A

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