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One-Dimensional Motion

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  1. One-Dimensional Motion Introduction to Displacement and Velocity

  2. Objectives • Define and calculate displacement • Differentiate between displacement and distance • Solve velocity problems • Differentiate between velocity and speed

  3. Displacement • Straight-line distance between the initial and final points • Has direction and magnitude • Δx, xf-xi • X represents position • Can be positive or negative • Measured in ft, m, km, etc

  4. Distance • Not the same as displacement • Only has magnitude, no direction • Always greater than or equal to displacement

  5. Examples • If I walk 2 m east, what is my displacement? • If walk 2 m east and 2 m west, what is my displacement? • Graph

  6. Vectors Vs Scalars • Vectors- Quantities that have magnitude and direction • Scalars-quantities that only have magnitude • Resultant- vectors added together

  7. Velocity • Change of position of an object over an interval of time • V=Δx/Δt= xf-xi/t f-t I • Has magnitude and direction • Vector or scalar?

  8. Example • Ms. K takes her dog Zeus for a walk. If they walk for 27 min and travel 1.89 km east, what is their average velocity in meters/sec?

  9. Speed • The change in distance over an interval of time • Speed=Δx/Δt= xf-xi/t f-t I • Only has magnitude no direction! • Vector or scalar? • They are the same only when moving in a straight line

  10. Example 1 • Polar Bears are extremely good swimmers with an average speed of 2.6 m/s, how far will it have traveled after 2.0 minutes?

  11. Example 2 • Ms. K and Zeus embark on a walk. If they leave Ms. K’s house, travel a distance of 1.2 km and return to the house in 12 minutes and 13 seconds, A) what was their average velocity? B) What their average speed? Give your answer in m/s

  12. Example 3 • Zeus and Ms. K embark on a southbound journey. First they walk south at 6.5 km/hr for 1.1 hours. Then they stop to take a nap for 18 minutes and then continue south at 5.5 km/hr for 1.2 hours. A) What was their average velocity? B) What was their displacement?

  13. Example 4- Honors • To qualify for the finals in a racing event a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/hr, what minimum average speed must it have in the second half of the event to qualify?

  14. One-Dimensional Motion Graphing Position as a function of time

  15. Objectives • Draw and interpret distance versus time graphs • Interpret what the slope indicates • Differentiate between average velocity and instantaneous velocity

  16. Distance Versus Time Graph • Distance Time What is slope? The symbol? What does the slope here indicate?????

  17. Example • Distance Time • What is the slope? What is the velocity?

  18. Example • Distance Time • What is the slope? What is the velocity?

  19. Example • Distance Time • What is the slope? What is the velocity?

  20. Example • Distance Time • What does this indicate about the velocity of the object at each part?

  21. Instantaneous Velocity • Instantaneous velocity-velocity at a specific point in time • Examples? • Average Velocity-velocity over a time duration • Example?

  22. Example Distance 4m 2m 5 10 15 20 time (seconds) What is the velocity between 0-5 seconds? Instant or average?

  23. Example Cont Distance 4m 2m 5 10 15 20 time (seconds) What is the velocity between 5-10 seconds? Instant or average?

  24. Example Cont Distance 4m 2m 5 10 15 20 time (seconds) What is the velocity at 6 seconds? 9.8 seconds? Instant or average? What is the velocity for 0-20 seconds?

  25. One-Dimensional Motion Acceleration

  26. Objectives • Define acceleration • Solve acceleration problems • Draw and interpret velocity versus time and acceleration versus time graphs

  27. Acceleration • The rate that velocity changes, so the change in velocity over the change in time • a= Δv/Δt= V f – V i/ t f – t I • Units- m/s2 • Vector or scalar?

  28. Example • A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?

  29. Example • I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds

  30. Instantaneous Versus Average • Average acceleration-change in velocity over an interval of time • Instantaneous Acceleration-change in velocity at an instant of time

  31. Example • A runnerstarts at a velocity of -1.2 m/s and speeds up constantly during a workout. After 25 minutes the treadmill has a velocity of -6.5 m/s. What is the average acceleration during this time?

  32. Velocity Versus Time Graph • Velocity • Time • Slope=rise over run • What does slope indicate here? • What about other types of graphs?

  33. Example • Velocity • Time • What does this tell us about the acceleration?

  34. Example Continued • Accel • time Acceleration is __________ and is below the time axis because _________________

  35. Example Continued • What does the distance versus time graph look like?

  36. Example • Velocity • Time • Draw the acceleration vs time graph and the position vs time

  37. One-Dimensional Motion Uniformly Accelerated Motion

  38. Objectives • Solve problems using uniform acceleration equations

  39. Uniformly Accelerated Motion • Acceleration is constant • What would a velocity versus time graph look like with constant acceleration? Without constant? • Equations • V f = V i+ at • Δx = V iΔt + ½ (a t2) • Vf2 = Vi2 + 2 a Δx • Δx = ½ (Vf – Vi) Δt • What variables do we have?

  40. Example • How long must a runway be for a plane to reach a takeoff velocity of 75 m/s if it accelerates at 20 m/s2?

  41. Example • My tea tumbler falls off my car and slides along 95 South for 75 m. Friction slows my tumbler at 6 m/s2. • A)How fast was the car moving when the tumbler fell? • B)How long did it take the tumbler to stop?

  42. One-Dimensional Motion Freefall

  43. Objectives • Define freefall • Solve freefall problems

  44. Freefall • If the only force acting upon an object is gravity the object is said to be in freefall • No _________________ • Considered to be uniform accelerated motion • g is the acceleration due to gravity= 9.8 m/s2 • When an object is in freefall we will use -9/8 m/s2 • Does mass matter? • What would a distance versus time graph look like for a ball being thrown in the air?

  45. Example • A ball is dropped from a height of 2.0 m. What is the velocity before it strikes the ground? How long did it take to hit the ground?

  46. Example Cont • Draw the position, velocity, and acceleration graphs

  47. Example continued • How long would it take for the same ball to be thrown up 2m and then fall to the ground?

  48. Example • A ball is thrown straight down with a speed of 0.50 m/s from a height of 4.0 m. What is the speed of the ball 0.70 seconds after the ball is released?

  49. Example • A 0.25 kg baseball is thrown upward w/ a speed of 30 m/s. Neglect friction. What is the maximum height that the baseball reaches?