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# 1.2 displacement and position vs time graphs

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IB physics - displacement

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### 1.2 displacement and position vs time graphs

1. 1. LECTURE 2 Displacement Position vs time plots IB Physics Power Points Topic 2 Kinematics www.pedagogics.ca
2. 2. Displacement Displacement is defined as the straight line path between an object’s initial position and an object’s final position. Displacement is a measurement of the change in position of a moving object. Displacement is not necessarily the distance travelled! s = 7 km [E] (displacement) s = 12 km (distance)
3. 3. Displacement (continued) Victor begins his walk 3 km [S] of Starbucks. 2 hours later, he ends his walk at his friend’s house 2 km [N] of Starbucks. What is Victor’s displacement? - x direction South +x direction NorthStarbucks ref pt We can see that Victor’s change in position equals 5 km [N]
4. 4. Displacement (continued) Mathematically, Victor’s displacement (Δs) can be calculated by : Displacement = change in position = final position – initial position - x direction South +x direction NorthStarbucks ref pt Initial position 3 km [South] Final position 2 km [North] Δs = sfinal – sinitial = 2 km [N] – 3 km [S] = 2 km [N] – -3 km [N] = 5 km [N] 5 km [N]
5. 5. Displacement (continued) Starbucks final position Initial position 3 km [South] House 2 km [North] Δs = sfinal – sinitial = zero – 3 km [S] = zero – -3 km [N] = 3 km [N] Victor picks up his friend and they take 1 hour to walk back to Starbucks for a coffee. What is Victor’s displacement relative to his starting point?
6. 6. Displacement (continued) -3 -2 -1 0 1 2 3 0 1 2 3 4 time (hrs) Position[N]km We can also show Victor’s walk on a position vs time graph Start Friend’s house Starbucks (reference pt.)
7. 7. -3 -2 -1 0 1 2 3 0 1 2 3 4 time (hrs) Position[N]km How far did Victor walk? Start Friend’s house Starbucks 5 km + 2 km = 7 km (DISTANCE)
8. 8. -3 -2 -1 0 1 2 3 0 1 2 3 4 time (hrs) Position[N]km What is Victor’s change in position? Start Friend’s house Starbucks = 3 km [N] (DISPLACEMENT)
9. 9. More about position vs time graphs Biff walks down the hallway and travels a constant 1.5 m [North] each second. What would a position vs time graph look like? 0 2 4 6 8 10 0 1 2 3 4 5 6 7 time (s) Position[N]m Biff is changing his position by 1.5 m [N] each second he walks.
10. 10. More about position vs time graphs Biff’s average velocity is 1.5 ms-1 [N]. How is this value related to the graph? 0 2 4 6 8 10 0 1 2 3 4 5 6 7 time (s) Position[N]m Δs = 9 m Δt = 6 s      -1 9 m 6 s 1.5 ms s slope t
11. 11. KEY CONCEPT: DON’T EVER FORGET THIS The slope of line connecting any two points on a position vs time graph represents the average velocity (speed). If the slope of a position vs time graph changes, then the velocity MUST also be changing.
12. 12. An example: Determine the velocity for each segment of this position vs time graph /m [N] s /s t A = 3 ms-1[N] B = 0 ms-1 C = -4 ms-1[N] or 4 ms-1[S] D = 0 ms-1 E = 6 ms-1[N] F = 0.9 ms-1[N]
13. 13. What have we learned so far about position vs time graphs? Slope indicates velocity (speed) A steeper slope indicates a greater velocity. A slope of zero (horizontal) means object is not moving (at rest). Negative slopes mean the object is moving in the opposite direction.
14. 14. 0 100 200 300 400 500 600 0 5 10 15 t /s s/m[downwards] Now consider a graph of a falling ball (strobe analysis lab): The graph is a curve. What does that mean? The slope of the tangent line represents the instantaneous velocity at t = 5 s. We can estimate the slope at any point by drawing a tangent to the curve. Let’s draw a tangent at t = 5 s
15. 15. 0 100 200 300 400 500 600 0 5 10 15 t /s s/m[downwards]By drawing two simple tangents, we can see that the slope of the tangent line increases as the ball falls. Slope represents velocity and it makes sense that a falling ball speeds up!!!
16. 16. 0 100 200 300 400 500 600 0 5 10 15 t /s s/m[downwards] Average velocity is defined as the overall displacement divided by the time. The average velocity between any two times would be the slope of a line connecting those points. The slope of this line represents the average velocity for the time interval 0 to 10 s
17. 17. Consider a trip downtown. You may drive on the expressway, on local streets, and you will stop at red lights. A trip might look like this. Determine the average speed for the entire trip? 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 time (min) Position(km) 0.6 km/min