Introduction to Position, Distance, and Displacement PDF

Introduction to Position, Distance, and Displacement SPH3U1 Kinematics A. Reading Positions: When objects start moving, it is useful to be able to describe an object’s location. To describe location, imagine a meter stick/number line is placed next to the object. Objects...

Introduction to Position, Distance, and Displacement SPH3U1 Kinematics A. Reading Positions: When objects start moving, it is useful to be able to describe an object’s location. To describe location, imagine a meter stick/number line is placed next to the object. Objects to the right of the zero (0) have positive positions Objects to the left of the zero (0) have negative positions Examples: Meters A. What is the position of the lightning bolt? _________________________________ B. What is the position of the happy face? _________________________________ C. What is the position of the sun? _________________________________ Use the number line below to give the positions of the objects (Don’t forget units!): Meters 1. What is the position of the heart? __________________________________________ 2. What is the position of the diamond? __________________________________________ 3. What is the position of the cross? __________________________________________ B. Locating Positions: Draw the object at the indicated locations. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 4. Put an “s” at the 2 m mark. 5. Put a “d” at the -6 m mark. 6. Put a “k” at the 7 m mark. 7. Put an “e” at the –1 m mark. SPH3U1 KinematicsC. Changing Positions:  Objects often moves or change positions. Find the initial and final positions of the frog. final initial -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 8. What is the initial position of the frog? 9. What is the final position of the frog? 10. If the frog traveled in a straight line from the initial position to the final position, what distance did it travel? D. Distance and Displacement: Now we will learn about two words that seem similar, but have different meanings in physics. Distance: measurement of the actual path traveled Displacement: the straight-line distance between 2 points If an object travels in one direction in a straight line, the distance traveled is EQUAL to the displacement Often, objects do not travel in straight lines (or they move back and forth), so the distance and displacement are NOT EQUAL. Examples: Bessie the cow and Sally the bird both traveled from point “A” to point “B.” Sally traveled in a straight line and Bessie did not. 10 meters B 25 meters A. What distance does Bessie the cow travel? _____________________ B. What distance does Sally the bird travel? _____________________ C. What is Bessie the cow’s displacement? _____________________ D. What is Sally the bird’s displacement? _____________________ SPH3U1 Kinematics  the track is 100 meters around 11. If the car travels once around the racetrack, what distance does it travel? 12. If the car travels twice around the racetrack, what distance does it travel? 13. If the car travels once around the racetrack, what is its displacement? E. Showing Displacement: When an object moves, an arrow can be drawn to show the displacement, the arrow points in the direction of motion. The arrow points from the starting position to the ending/final position; arrow should be straight Examples: ✓ A school bus final initial ✓ A bike moving along a number line, from a position of 4 m to –3m initial final -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters ✓ Any object, using “ ⃗ “to represent the initial position and “ ⃗ “to represent the final position. In this case, the object moves from the –6 m position tothe 3 m position.  SPH3U1 Kinematics 14. Draw an arrow showing an object that moves from the –4 m position to the 5 m position. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 15. Draw an arrow showing an object that moves from the 7 m position to the 1 m position. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters F. What About Direction? ❖ Displacement also includes direction! Possible directions include: ✓ positive or negative ✓ left or right ✓ up or down ✓ north or south, east or west ❖ In this class, we will often use positive and negative to show direction. ✓ A displacement is negative if the arrow points to the left or down ✓ A displacement is positive if the arrow points to the right or up -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 16. Is the above displacement positive or negative? _____ G. Calculating Displacement: Remember: Displacement is the straight-line distance between 2 points. To give a displacement we should give both the magnitude (size) and the direction. To find the magnitude of the displacement, count the number of spaces from the initial position to the final position. The following shows a displacement of ______________  Meters SPH3U1 Kinematics ❖ The following shows a displacement of ______________ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters ❖ The following shows a displacement of ______________ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters Use the number line below to answer the following questions: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 17. Draw an arrow to show the displacement. 18. Is the initial position positive or negative? 19. Is the final position positive or negative? 20. Is the displacement positive or negative? 21. What is the displacement [magnitude (with units) and direction]? ______ Use the number line below to answer the following questions: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 22. Draw an arrow to show the displacement. 23. Is the initial position positive or negative? 24. Is the final position positive or negative? 25. Is the displacement positive or negative? 26. What is the displacement [magnitude (with units) and direction]? _______________ SPH3U1 Kinematics -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters 27. Use the above number line to help answer the following question: Freddy the cat started at the –3 m position. He then walked to other locations. Mark each new location with the letter for that part. a. Freddy started at the –3 m position. (mark this position with an “a”) b. First, Freddy walked 2 meters in the positive direction (right) to the –1 m position. c. Second, Freddy walked 5 meters in the positive direction to the +4 m position. d. Third, Freddy walked 1 meter in the negative direction to the +3 m position. e. Finally, Freddy walked 8 meters in the negative direction to the –5 m position. f. Draw a displacement arrow that starts at Freddy’s initial position (-3 m) and ends at Freddy’s final position (-5 m). g. What was Freddy’s total displacement? (For this, you only need to look at his initial and final position). Be sure to include the magnitude, direction and units. h. To get the distance Freddy traveled, add up all the distances: 2m+5m+1m+8m=m i. Is Freddy’s total displacement equal in size to Freddy’s total distance traveled? Explain.