Position and Displacement Definition Position x the location

Position and Displacement

Definition Position (x) – the location of an object with respect to a specified reference point. *We choose this reference point to be the origin of a coordinate system. A km -3 -2 -1 0 1 6 7 8 9 10 The position of particle “A” is either x = -3 or x = 6, depending on which reference point (or origin) you use.

Definition Displacement (Dx) – the change in an object’s position during a time interval. Dx = x 2 – x 1 or Dx = xf – xi These are all VECTORS. What’s a vector? *Displacement must have both a magnitude (size) and a direction (right, left, up, down, north, south, etc).

A B C meters -3 -2 -1 0 1 Using the number line above, find the distance travelled and the displacement in moving from - A to B - C to A 1 m, 1 m [right] Dx = 1 – (1 m) = 0 m 4 m, 4 m [left] - A to C and then back to A 8 m, 0 m - C to B, passing through A 4 m, 3 m [left] Dx = (-2) – (1 m) = -3 m OR 3 m [left]

Definition Average Velocity ( v ) – the displacement of an object divided by the elapsed time. v = Dx/Dt (or v=Dx/t)

A D B C Find Sam’s avg. speed and avg. velocity for the entire trip. Sam runs the 400 m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100 m long. His average speed during each interval are as follows. AB: 7 m/s BC: 8 m/s CD: 6 m/s DA: 7. 5 m/s s = d/t t = d/s = 100 m/7 sec = 14. 286 sec 100 m/8 sec = 12. 5 sec 100 m/6 sec = 16. 667 sec 100 m/7. 5 sec = 13. 333 sec Avg Velocity = 0 s = d/t = (400 m)/(56. 786 s) = 7. 04 m/sec since Dx = 0 for the entire trip.

HONORS ONLY!!! A D 104. 94 31. 831 m B 100 C Find Sam’s average speed and average velocity for the 1 st half of the race. Sam runs the 400 m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100 m long. His average speeds during each interval are as follows. AB: 7 m/s, 14. 286 sec BC: 8 m/s, 12. 5 sec CD: 6 m/s, 16. 667 sec DA: 7. 5 m/s, 13. 333 sec s = d/t t = d/s = 200 m/(14. 286+12. 5 s) = 7. 47 m/s v = Dx/t = (104. 94 m )/(14. 286+12. 5 s) = 3. 92 m/sec