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Linear Motion and Displacement in Physics

Explore the concepts of motion relative to reference objects, displacement, distance, speed, velocity, and acceleration. Learn how to calculate and differentiate between them in various scenarios.

michaelvgarcia
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Linear Motion and Displacement in Physics

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  1. Chapter 2 Linear Motion

  2. Motion Is Relative • Motion is relative to an object of reference. Speed is zero relative to the Earth but 30 km/s relative to the Sun

  3. Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you and the other is 3 meters upstream from you. Which can you swim to in the shortest time? 1. The preserver upstream. 2. The preserver downstream 3. Both require the same.

  4. 1. The preserver upstream.2. The preserver downstream3. Both require the same. Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you and the other is 3 meters upstream from you. Which can you swim to in the shortest time?

  5. Displacement • Distance d: position, location • Displacement Δd: change in position • 1m= original (initial) location • 4 m = final location • Displacement Δd = 4m – 1m = 3m 1m 4m

  6. Displacement • Displacement: change in position • 4m= original (initial) location • 1m = final location Displacement Δd = 1m – 4m = - 3m 1m 4m

  7. Displacement, Distance • Distance traveled usually different from displacement. • Distance always positive. • Previous example: always 3 m.

  8. Distance Distance is the path length traveled from one location to another. It will vary depending on the path. What is the displacement in the round trip bellow? Answer: 0 Km

  9. What is the displacement in the situation depicted bellow? • a) 3 m b) 6 m c) -3 m d) 0 m 1m 4m

  10. What is the distance traveled in the situation depicted bellow? • a) 3 m b) 6 m c) -3 m d) 0 m 1m 4m

  11. Speed Unit: m/s, km/h Definition: Abbreviations commonly used: d = distance t = time v = speed Instantaneous Speed: speed at any instant in time. Definition: Ex.: You drive 320 km in 4 hours. What is the average speed?

  12. Distance Total distance covered: average speed x time Ex. Distance = 40 km/h x 6 h = 240 km 40 Km/h 240 Km

  13. Velocity Velocity = speed + direction Example: The wind blows with 40 km/h – towards the East… Definition:

  14. Velocity Negative Ex. -60 km/h Positive Ex. +80 km/h Direction of motion

  15. Constant Velocity velocity = slope of graph position vs. time = displacement/time Rise= v = 8m/2s = 4 m/s Run

  16. Acceleration Acceleration: change in the state of motion. Definition: Example: A car changes its velocity from 30 km/h to 40 km/h in 2 s. What is its acceleration?

  17. Deceleration Decrease of velocity caused by negative acceleration (deceleration)

  18. Acceleration on Galileo’s Inclined Planes A ball rolling down the plane will pick up the same amount of speed each successive second. Example: 2m/s for each 1s Time (s) Speed m/s Acceleration = 2m/s/s Velocity= Acceleration x Time v=at Greater Acceleration for steeper inclined planes

  19. Acceleration velocity = at = 9 km/hs x 2s = 18 km/h Final Velocity = Initial Velocity + Acceleration x Time Interval v=vo + at

  20. Deceleration, Example velocity = 28m/s – 5 m/s2 x (12s – 9s) = 13 m/s

  21. Distance Traveled In Motion with Constant Acceleration Distance = average velocity x time Starting from rest: Average velocity = (0 + at)/2 (with initial velocity vo

  22. Tracks A and B are made from pieces of channel iron of the same length. They are bent identically except for a small dip near the middle of Track B. When the balls are simultaneously released on both tracks as indicated, the ball that races to the end of the track first is on 1. Track A.2. Track B. 3. Both reach the end at the same time.

  23. 1. Track A.2. Track B.3. Both reach the end at the same time. Tracks A and B are made from pieces of channel iron of the same length. They are bent identically except for a small dip near the middle of Track B. When the balls are simultaneously released on both tracks as indicated, the ball that races to the end of the track first is on

  24. A motorist wishes to travel 40 kilometers at an average speed of 40 km/h. During the first 20 kilometers, an average speed of 40 km/h is maintained. During the next 10 kilometers, however, the motorist averages only 20 km/h. To drive the last 10 kilometers and average 40 km/h, the motorist must drive 1. 60 km/h. 2. 80 km/h. 3. 90 km/h.4. faster than the speed of light.

  25. 1. 60 km/h. 2. 80 km/h. 3. 90 km/h.4. faster than the speed of light. A motorist wishes to travel 40 kilometers at an average speed of 40 km/h. During the first 20 kilometers, an average speed of 40 km/h is maintained. During the next 10 kilometers, however, the motorist averages only 20 km/h. To drive the last 10 kilometers and average 40 km/h, the motorist must drive

  26. An airplane makes a straight back-and-forth round trip, always at the same airspeed, between two cities. If it encounters a mild steady tailwind going, and the same steady headwind returning, will the round trip take: 1. more2. less3. the same time as with no wind?

  27. 1. more2. less3. the same time as with no wind? An airplane makes a straight back-and-forth round trip, always at the same airspeed, between two cities. If it encounters a mild steady tailwind going, and the same steady headwind returning, will the round trip take:

  28. Galileo’s Formula Eliminate time: Starting from rest. With initial velocity.

  29. Example Take Off • The minimum takeoff speed for a certain airplane is 75 m/s. What minimum acceleration is required if the plane must leave a runway of length 950 m? Assume the plane starts from rest at one end of the runway. • (a) 1.5 m/s2 • (b) 4.5 m/s2 • (c) 7.5 m/s2 • (d) 3.0 m/s2 • (e) 6.0 m/s2

  30. Motion Graphs Motion with constant velocity starting from origin: Slope = speed Dist. = speed x time Faster=steeper slope

  31. Graph of Motion with Constant Acceleration v a = 4 m/s2 x = 4t2/2

  32. Free Fall Objects fall freely with an acceleration g=9.8 m/s2 (often rounded up to 10 m/s2) Speed gained during free fall: v=gt Distance Traveled: Galileo:

  33. What goes up, must come down…An object thrown upward: • slows at a rate of g… • then has zero velocity as it changes its direction from up to down. • then falls speeding up at a rate of g. • equal elevations have same speed (but opposite direction)

  34. Application: “Hang-time” of jumpers Michael Jordan’s best hang-time was 0.9 s Round this to 1 s. How high can he jump? Use d = ½ g t2 . For 1 s hang-time, that’s ½ s up and ½ s down. Substituting ½ = 0.5 seconds into the distance equation d = ½ (10) (0.5)2 = 1.25 m This is about 4 feet!

  35. Acceleration Problem • Two cars start simultaneously when the stop light turns green, with the accelerations of 2m/s2 and 3 m/s2 respectively. • a) What are the velocities of the cars after 3 s? • b) What is their relative velocity after 3 s? • c) What is the distance between the cars after 3s? v = 2 x 3 = 6m/s a) v = at v = 3 x 3 = 9m/s b) relative velocity = 9-6 = 3m/s d1 = ½ 2 x 9= 9m c) d = ½ at2 d2 = ½ 3 x 9= 13.5m distance between cars: 13.5 – 9 = 4.5 m

  36. Summary:

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