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Unit 1: Linear Motion

Learn about linear motion and key concepts such as distance, displacement, speed, and velocity. Discover the difference between distance and displacement, how to calculate average speed and velocity, and understand their relevance in everyday life. Suitable for physics students and anyone interested in understanding linear motion.

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Unit 1: Linear Motion

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  1. Unit 1: Linear Motion Sprayberry Physics

  2. Physics Comp Book UNIT 1: Linear Motion (@top, BIG!) p. 1 Copy GPS listed on the LTA. Circle the verbs; underline the nouns. • PageContents 2 Concept Map: Linear Motion pt. 1 3 linear motion, distance 4 displacement, speed 5 velocity, acceleration 6 Venn Diagram: Scalar vs. Vector 7 Concept Map: Linear Motion pt. 2 8 Lab SUMUPS: * Distance vs. Displacement * Froggy

  3. vertical horizontal Let’s do a Frayer model for linear motion: Definition: Drawing: Motion in a straight line linear motion What it’s NOT: How to remember:

  4. Concept Map: Linear Motion p. 2when an object moves we observe— which is calculated by called called which is calculated by which is calculated by called called which is calculated by which is calculated by called The position changing How quickly the position changes The rate at which the movement changes

  5. When an object moves, we can observe: For your concept map on p.2 of comp book! • The position changing • Distance: how far it travels is called (in meters) • Displacement: how far its position is from the starting point (in meters with a direction) • How quickly the position changes • Speed: how fast it’s covering distance (or how much distance is covered in an amount of time) • Velocity: how fast it’s position is moving and in what direction relative to some other point (like home or a destination • The rate at which the movement changes • Acceleration: is it speeding up or slowing down

  6. Displacement Isn’t Distance • The displacement of an object is not the same as the distance it travels • Example: Throw a ball straight up and then catch it at the same point you released it • The distance is twice the height • The displacement is zero

  7. Distance & Displacement

  8. Distance & Displacement C 4 m B 5 m 3 m You walk from A to B to C. What is your distance traveled? What is your displacement from A? A Your distance traveled is 7m Your displacement form A is 5 m

  9. Let’s do Frayers for distance & displacement in your comp book: How to calculate: Definition: How to remember: Don’t confuse this with:

  10. Types of Speed • Instantaneous Speed is the speed at any specific instance or moment in time • Ex. On a speedometer reading… you are traveling 35 mph (mi/hr) or 50 km/h or 25 m/s • Average Speed is the total distance covered divided by total time

  11. How do you calculate average speed? • The average speed of an object is defined as the totaldistance traveled divided by the total time elapsed • OR take the average: (initial speed + final speed) 2 • Speed is a scalar quantity … why is it not a vector?

  12. Speed, cont • Average speed totally ignores any variations in the object’s actual motion during the trip • The total distance and the total time are all that is important • SI units are m/s

  13. Speed & Velocity • Speed is the distance traveled in a certain time. • Velocity is the displacement traveled in a certain time. • Velocity is speed in a given direction.

  14. Velocity • The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed • Velocity is a vector quantity

  15. Velocity • It takes time for an object to undergo a displacement • The average velocity is rate at which the displacement occurs • generally use a time interval, so let ti = 0

  16. Velocity, cont. • Direction will be the same as the direction of the displacement (time interval is always positive) • + or - is sufficient to indicate direction • Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) • Other units may be given in a problem, but generally will need to be converted to these

  17. Speed vs. Velocity • Cars on both paths have the same average velocity since they had the same displacement in the same time interval • The car on the blue path will have a greater average speed since the distance it traveled is larger

  18. Let’s do Frayers for speed & velocity in your comp book: How to calculate: Definition: Wait for the next slide How to remember: Don’t confuse this with:

  19. LIST (3) Equation • (2) LABEL w/units (4) Solve Speed vs. Velocity • You drive from Yakima to Seattle (140 miles away) • You stop in Ellensburg for a 2 hr lunch with a friend. • Your total driving time is 2 hours • What is the average speed? • What is the average velocity? (solve these questions in the Frayers)

  20. Constant Velocity • Constant velocity is constant velocity • The instantaneous velocities are always the same • All the instantaneous velocities will also equal the average velocity

  21. Velocity Example 1 North North 40º North of East

  22. How fast is the plane moving in respect to the ground? Velocity Example 2

  23. How fast is the plane moving in respect to the ground?Notice the two velocities are occuring in the same LINE (linear motion…) Velocity Example 2

  24. Is this linear motion?How fast is the plane moving in respect to the ground? Velocity Example 3

  25. How fast is the plane moving in respect to the ground? Velocity Example 3

  26. How fast is the plane moving in respect to the ground? Velocity Example 3

  27. Concept Map: Linear Motion p. 2when an object moves we observe— which is calculated by called distance called which is calculated by displacement which is calculated by speed called called which is calculated by velocity called which is calculated by acceleration Adding all the legs of the journey The position changing Xfinal –x initial Total distance Total time How quickly the position changes xfinal –x initial time The rate at which the movement changes vfinal –v initial time

  28. Scalar vs. Vector • Scalar - magnitude only and units (e.g. volume, mass, time, speed, distance) magnitude means SIZE, units: like meter, mile, etc. • Vector – magnitude, units & direction (e.g. weight, velocity, acceleration) in other words: where is this “thing” pointing?

  29. Pictorial Representation • An arrow represents a vector • Length = magnitude (size) of vector • Direction = direction of vector

  30. Pictorial Representation • This arrow could represent a vector of magnitude 10 point to the “right” • This arrow could represent a vector of magnitude 5 point to the “left”

  31. Get your comp book… • Draw an empty Venn Diagram like this on p. 6

  32. Magnitude Size Direction Units Distance Displacement Speed velocity Acceleration Mass Weight 12 cm 47 kg (mass) 470 Newtons (weight) 50 meters 50 meters West 25 m/s 25 m/s toward home 25 m/s away from home 10 m/s2 10 m/s2 toward the ground Label one side scalar, other vector Place these words in the correct space on the diagram:

  33. Acceleration • Change in velocity divided by the change in time

  34. Acceleration Great animation showing acceleration: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm • Changing velocity (not constant) means an acceleration is present • Acceleration is the rate of change of the velocity (how fast the velocity changes) • Units: m/s2 (SI) other examples:cm/s2 ft/s2

  35. Average Acceleration • Vector quantity • When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing • When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

  36. Relationship Between Velocity & Acceleration • Uniform velocity (shown by red arrows maintaining the same size) • Acceleration equals zero

  37. Relationship Between Velocity & Acceleration • Velocity and acceleration are in the same direction • Acceleration is uniform (blue arrows maintain the same length) • Velocity is increasing (red arrows are getting longer) • Positive velocity and positive acceleration

  38. Relationship Between Velocity & Acceleration • Acceleration and velocity are in opposite directions • Acceleration is uniform (blue arrows maintain the same length) • Velocity is decreasing (red arrows are getting shorter) • Velocity is positive and acceleration is negative

  39. Let’s do a Frayer for acceleration in your comp book: How to calculate: Definition: Wait for the next slide How to remember: Don’t confuse this with:

  40. LIST (3) Equation • (2) LABEL w/units (4) Solve Acceleration Example 1 (solve this problem in the Frayer section…) • A car is moving at a speed of 35.8 m/s. If it takes 2.0 s to come to a complete stop, what acceleration would it have?

  41. LIST (3) Equation • (2) LABEL w/units (4) Solve Acceleration Example 2 • A car is said to go "zero to sixty in six point seven seconds". What is its acceleration in m/s2?

  42. Acceleration Example 3 • The driver from the previous problem can't release his foot from the gas pedal. (The gas pedal is also known as the accelerator. Coincidence? I think not.) How many additional seconds would it take for the driver to reach 80 mph? (assuming the acceleration hasn't changed)? • LIST (3) Equation • (2) LABEL w/units (4) Solve

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