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Motion in One DImension

Motion in One DImension. Chapter 2. Displacement and Velocity. One Dimensional Motion. To simplify the concept of motion, we will first consider motion that takes place in one direction. One example is the motion of a commuter train on a straight track .

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Motion in One DImension

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  1. Motion in One DImension Chapter 2

  2. Displacement and Velocity

  3. One Dimensional Motion • To simplify the concept of motion, we will first consider motion that takes place in one direction. • One example is the motion of a commuter train on a straight track. • To measure motion, you must first choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time. • In the train example, any station along the route.

  4. Displacement • Displacement is a change in position. • Displacement is not always equal to the distance traveled. • The SI unit of displacement is the meter, m. ∆ x = xf -xi Displacement – final position – initial position

  5. Displacement is not always equal to the distance traveled. Example: If a gecko starts at an initial position of 20 cm and moves to the 80 cm mark, then retreats back to the 50 cm mark as its final position, How far has the gecko traveled? What is its displacement? The gecko traveled 90 cm, but its displacement is 30 cm.

  6. Positive and Negative Dispacement • In this course, right (east) is positive as well as upward (north) and left (west) is negative as well as downward (south).

  7. Average Velocity Average velocity is the total displacement divided by the time interval during which the displacement occurred. In SI, the unit of velocity is meters per second abbreviated as m/s.

  8. Example: • Consider a trip to a friend’s house 370 km to the west (negative direction) along a straight highway. If you left at 10 AM and arrived at 3 PM, what is your average velocity? This is your average. You did not travel at 74 km/h at every moment.

  9. Your turn… During a race on a level ground, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s dispacement after 137 s? x = v t = 6.02m/s • 137s = 825 m

  10. Velocity vs. Speed • Velocity is not the same as speed. • Velocity describes motion with both direction and a numerical value (magnitude). • Speed has no direction, only magnitude. • Average speed is equal to the total distance traveled divided by the time interval.

  11. Interpreting Velocity Graphically • Consider an object whose position-time graph is not a straight line, but a curve. • We obtain different average velocities depending on the time interval. The instantaneous velocity is the velocity of the object at a specific point in the object’s path The instaneous velocity can be determined by measuring the slope of the line that is tangent to that point on the diatance-vs-time graph.

  12. Practice Problems 2A • Problems 1-6, Page 44

  13. Acceleration

  14. Changes in Velocity • Acceleration – Rate at which velocity changes over time • An object accelerates if its speed, direction or both change. • Acceleration has direction and magnitude. • Acceleration is a vector quantity.

  15. Acceleration has the dimensions of lengthdivided by time squared. • SI units are m/s2 • Remember we have (m/s)/s = m/s2 Acceleration

  16. Example: A bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow down from 9.0 m/s to a complete stop?

  17. Your turn… • A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? • A treadmill runs with a velocity of -12m/s and speeds up at regular intervals during a half hour workout. After 25 minutes, the treadmill has a velocity of -6.5 m/s. What is the acceleration of the treadmill during this period?

  18. Changes in Velocity • Consider a train moving to the right, so that the displacement and velocity are positive. • The slope of the velocity-time graph is the average acceleration. • When the velocity in the positive direction is increasing, the acceleration is positive, as at A. • When the velocity is constant, there is no acceleration, as at B. • When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.

  19. Velocity and Acceleration

  20. Motion with Constant Acceleration • When velocity changes by the same amount during each time interval, acceleration is constant. • The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide.

  21. These equations apply to any object moving with constant acceleration. These equations use the following symbols:

  22. Equations for Constantly Accelerated Straight-line Motion

  23. Examples: • A racing car reaches a speed of 42 m/s. It begins a uniform negative acceleration , using its parachute and braking system, and comes to a complete rest 5.5 s later. Find the distance that the car travels during braking.

  24. Your turn… • A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance traveled during this time. • A driver in a car at a speed of 21.9 m/s sees a cat 101 m away on the road. How long does it take the car to accelerate uniformly to a stop in exactly 99m? • A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast (in m/s) is the car moving after this time?

  25. …more practice A plane starting at rest at one end of the runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to takeoff? A car starts from rest and travels for 5.0 s with a constant acceleration of -1.5m/s2 . What is the final velocity of the car? How far does the car travel in this time interval?

  26. Final velocity after any distance problem A person pushing a stroller starts from rest , uniformly accelerating at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?

  27. Final velocity after any distance problem - solution

  28. Your turn… A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration is 2.7m/s2 , how far did it travel during the acceleration? A car traveling initially at 7.0 m/s accelerates uniformly at the rate of 0.80 m/s2 for a distance of 245 m. What is the velocity at the end of the acceleration? What is the velocity after it accelerates for 125 m? What is the velocity after it accelerates for 67 m?

  29. Practice Problems 2B-2E • Pages 49 (1-5), 53 (1-4), 55 (1-4) and 58 (1-6)

  30. Falling Objects

  31. Free Fall August 2, 1971 – On the moon With NO air resistance objects will fall at exactly the same rates Fall with the same constant acceleration. Free fall is the motion of a body when only gravity is acting on it. The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration. Free-fall acceleration is denoted with the symbols ag or g

  32. Free Fall Acceleration • Free-fall acceleration is the same for all objects regardless of mass. • We will use the value g = 9.81 m/s2 • Free-fall acceleration on Earth’s surface is • -9.81 m/s2 at all points in the object’s motion. Consider a ball thrown up into the air. • Moving upward: velocity is decreasing, acceleration is -9.81 m/s2 • Moving upward: velocity is decreasing, acceleration is -9.81 m/s2 • Moving upward: velocity is decreasing, acceleration is -9.81 m/s2

  33. Falling Object Example Jason hits a volleyball so that it moves with an initial velocity of 6.0m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor?

  34. Falling Object Example solution Both ∆t and vfare known. Therefore, first solve for vfusing the equation that does not require time. Then, the equation for vf that does not involve time can be used to solve for ∆t .

  35. Plug and Chug

  36. Your turn… A flowerpot falls from a windowsill 25.0m above the sidewalk. How fast is the flowerpot moving when it hits the ground? How much time would you have to move out of the way before the flowerpot hits the ground? A robot drops a camera off a 239m cliff on mars where free-fall acceleration is -3.7 m/s2 Find the velocity with which the camera hits the ground. Find the time required to hit the ground

  37. Practice Problems 2F • Page 64 Problems 1-4 Mixed Review pp 70-71 (33-41)

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