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Kinematics 1-D Motion

Kinematics 1-D Motion. Vocabulary of Motion. Distance Scalar quantity Displacement Vector quantity, Object’s change in position. 5 km. Distance traveled = 15 km Displacement = 5 km, East. 5 km. 5 km. Vocabulary of Motion. Speed Scalar Quantity - Change in distance over time .

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Kinematics 1-D Motion

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  1. Kinematics 1-D Motion

  2. Vocabulary of Motion • Distance • Scalar quantity • Displacement • Vector quantity, Object’s change in position

  3. 5 km • Distance traveled = 15 km • Displacement = 5 km, East 5 km 5 km

  4. Vocabulary of Motion • Speed • Scalar Quantity - Change in distance over time

  5. Vocabulary of Motion • Velocity • Vector Quantity • Average Velocity = v = Change in Position = Δd Change in Time Δt

  6. Vocabulary of Motion • Acceleration • Vector Quantity a = Change in Velocity = Δv Change in Time Δt • Positive a – speeding up • Negative a – slowing down

  7. Motion Graphs • Position Vs. Time Position Position Time Time v = + constant Object is Stopped, v = 0

  8. Position Vs. Time Position Time v = - constant

  9. (Not constant velocity) Position Position Time Time Object is decreasing speed over time

  10. Position Position Time Time Walks away. Stops, walks back towards start and keeps going past 0, -. Object is increasing speed over time

  11. Position Time Constant speed, slowing down to a stop, then increasing speed

  12. Slope? • The slope of a Position vs. Time graph is the objects Velocity! Slope = Δy = Δd = v Δx = Δt

  13. Which graph best represents the motion of a block accelerating uniformly down an inclined plane?

  14. Motion Graphs • Velocity vs. Time Velocity Velocity Time Time Velocity is constant Increasing at a constant rate, +

  15. Time Velocity Velocity Time Velocity is decreasing, stops and increases in the other direction Velocity is decreasing at a constant rate, -

  16. Slope? • The slope of a velocity vs. Time graph is its acceleration! Slope = Δy = Δv = a Δx = Δt

  17. Mathematical Analysis • Finding Average Velocity v = vi + vf or Δd 2 Δt Note: vi = Initial Velocity vf = Final Velocity

  18. Acceleration a = Δv or vf – vi Δt Δt

  19. Problems • A car travels 650 m in 5.0 sec. What is its average velocity??

  20. Problems • A car starting at rest accelerates at 2.0 m/s2 for 2.0 sec. What is its final velocity? • A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.

  21. Area Under Velocity vs. Time graph is the distance traveled

  22. Additional Motion Equations • d = vit + 1/2at2 • vf2 = vi2 + 2ad

  23. On Your Own • A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.

  24. FREE FALLING!

  25. Free Fall • All bodies fall at the same rate of acceleration • The acceleration due to gravity near the Earth’s surface is 9.81 m/s2

  26. What does that mean? • Every second an object falls, its speed is increasing by 9.81 m/s

  27. t = 0 sec, v = 0 m/s t = 1 sec, v = 9.81 (10) m/s t = 2 sec, v = 19.62 (20) m/s t = 3 sec, v = 29.43 (30) m/s

  28. Motion Graphs Position Velocity Time Time

  29. Mathematical Analysis of Free Fall • a = g = 9.81 m/s2 • For an object being dropped, The initial velocity is ZERO. • Motion in the y-direction (vertical)

  30. Problem . . . • A 100 kg object is dropped from 10 m. How long does it take to hit? • What is the final speed right before it hits the ground?

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