1. 1 Motion in 1D o Frames of Reference o Speed  average  instantaneous o Acceleration o Speed-time graphs and distance travelled Physics -I Piri Reis University 2010-2011

2. 2 Speed o Distance is the number of metres between two points o Time is the number of seconds it takes for something to happen o If a person walks a distance x metres in t seconds, then we define the persons walking speed, v, to be x /t m/s v = x /t o Strictly this is their AVERAGE speed whilst walking. o The distance travelled is then d = vt

3. 3 Speed o If only a short part of the walk is considered, say x 2 and that part takes a time t 2 to walk, then o the speed for that part of the walk could be different o Slower o or faster o If we keep reducing the size of x 2, then o the time t 2 will also get shorter o If we keep reducing x 2 until it becomes ~0, then o the time t 2 will also be ~0 o The ratio x 2 /t 2 is the INSTANTANEOUS speed. o This is then the derivative of the distance wrt t v = d x /dt ≈ x 2 /t 2 x x2x2

4. 4 Speed o Instantaneous speed is what is read from a car speedometer o Average speed is what matters for a long trip. o The average speed for each part of the trip is d i /t i o The average speed for the trip v = { ∑ x i } / { ∑t i } o The average speed is NOT s = { ∑ x i /t i } / 6 o because the distances are not necessarily equal d x6x6 x5x5 x4x4 x3x3 x2x2 x1x1

5. 5 Time, t Distance, x On a graph of time vs distance instantaneous speed is the slope The person started to walk at t = 0 from x = 0 Each point on graph shows Where they are at a given time Distance-time graphs

6. 6 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person walks with constant speed Distance, x

7. 7 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person walks with slowing speed Distance, x

8. 8 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person walks with increasing speed Distance, x

9. 9 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person speeds up and then slows down Distance, x

10. 10 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person walks with constant speed then stops Distance, x

11. 11 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Person stands still walks at constant speed then stops and stands still Distance, x

12. 12 time On a graph of time vs distance instantaneous speed is the slope Distance-time graphs Here the person changed Direction and walked backwards And forwards again Distance, x

13. 13 Time, t Distance, x Distance-time graphs At any point on the curve, the tangent is The instantaneous speed, v = d x /dt When the slope is negative the direction is backwards

14. 14 Acceleration o To change speed, the walker must accelerate o The average acceleration, a, is (Total increase in speed) (Time taken to change) o The instantaneous acceleration is the limit as the changes become small, just like speed instantaneous a = dv/dt = d 2 x /dt 2 a =

15. 15 Time, t Distance, x Acceleration on a distance-time graph At any point on the curve, the tangent is The instantaneous speed, v = d x /dt The curvature of the line tells about acceleration This curvature is deceleration This is acceleration

16. 16 Time, t Distance, x Acceleration on a distance-time graph At any point on the curve, the tangent is The instantaneous speed, v = d x /dt The curvature of the line tells about acceleration Zero acceleration deceleration acceleration Slope increasing Slope decreasing

17. 17 Time, t Speed, d x /dt Speed-time graph At any point on the curve, the tangent is The instantaneous acceleration, a = d 2 x /dt 2 This person is walking at constant speed (Acceleration is zero)

18. 18 Time, t Speed, v = d x /dt Speed-time graph At any point on the curve, the tangent is The instantaneous acceleration, a = d 2 x /dt 2 This person is accelerating Constantly

19. 19 Time, t Speed, d x /dt Speed-time graph At any point on the curve, the tangent is The instantaneous acceleration, a = d 2 x /dt 2 This person is accelerating but the rate of acceleration is decreasing

20. 20 The area under the curve in a speed-time plot is the distance travelled Time, t Speed, d x /dt Speed-time graph Recall x = vt for constant speed which, more generally, is x = ∫ d x /dt dt

21. 21 Time, t Speed, d x /dt Speed-time graph x = ∫ d x /dt dt x = 0.5 x t 0 x s max t0t0 s max In this case

22. 22 Time, t Speed, d x /dt Speed-time graph d = ∫ d x /dt dt In this case the curve can be broken into several triangles & squares to work out the distance travelled

23. 23 Time, t Speed, d x /dt Speed-time graph x = ∫ d x /dt dt t0t0 In this case the curve can be broken into several triangles & squares to work out the distance travelled t1t1 t2t2 t3t3 t4t4 t5t5 s4s4 s3s3 s2s2 s1s1

24. 24 Time, t Speed, dx/dt Speed-time graph x = ∫ d x /dt dt t0t0 In this case - good luck!

25. 25 Reference Frames o What something looks like depends on where you look from  big when close  small when far away o In physics it is very important to be clear about where you are looking from,  where you are sitting when you make a measurement,  Where you are imagining you are when you do a calculation o But what is important is not the distance, but the speed of where you are looking from.  We call the person who is looking ‘the observer’,  We call the place they are looking from ‘the reference frame’  It is called a ‘frame’ because we imagine a coordinate system with three axis, which looks like a ‘frame’.

26. 26 Frames can have Different origins If the frames are arranged to Be in the same orientation Then x 1 = x 2 + offset distance

27. 27 Frames can have Different rotations

28. 28 Frames can have Different speeds

29. 29 Different speeds is the most significant for what we will be doing

30. 30 Reference Frames o A reference frame is a ’place to look from’ o It is the coordinate system we are measuring from The speed of the blue car depends on where it is measured from Measured from the road it is V 1 Measured from the green car it is V 1 -V 2

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32. 32 Z.Akdeniz Reference Frames o In an elevator accelerating up the effective gravity is increased o Accelerating down the effective gravity is reduced o At a constant speed up or down there is no difference  This is a reference frame which moves with constant speed o If the elevator is in free fall, then there is ‘no gravity’ and the frame of reference is effectively an inertial frame  In fact it is accelerating, but then every frame is - gravity is everywhere in the universe

33. 33 Reference Frames o More about gravity in a couple of weeks.