1. Graphical representation Graphs 0 Clock reading t (s) Position x (m) t 0 = 0 t 1 = 20 t 2 = 40 t 3 = 60 t 4 = 80 t 5 = 100 t 6 = 120 x 0 = 0 x 1 = 100 x 2 = 200 x 3 = 300 x 4 = 400 x 5 = 500 x 6 = 600 X x,mx,m t, s 20406080100120 0 100 200 300 400 500 600 y = kx +b x = kt +b x = 5t +0 v=5m/s

2. Graphical representation Graphs 0 Clock reading t (s) Position x (m) t 0 = 0 t 1 = 20 t 2 = 40 t 3 = 60 t 4 = 80 t 5 = 100 t 6 = 120 x 0 = 640 x 1 = 500 x 2 = 360 x 3 = 220 x 4 = 80 x 5 = -60 x 6 = -200 X Describe in words the motion of the biker: 1.In what direction does he go? 2.What is the starting point of his motion? 3.What is his speed? 4.Does it change? 640

3. Graphical representation Graphs 0 Clock reading t (s) Position x (m) t 0 = 0 t 1 = 20 t 2 = 40 t 3 = 60 t 4 = 80 t 5 = 100 t 6 = 120 x 0 = 640 x 1 = 500 x 2 = 360 x 3 = 220 x 4 = 80 x 5 = -60 x 6 = -200 X Construct a position-versus-time graph for the bike trip. Write a function of the graph. x = 640 - 7t x, m t, s 20406080100120 0 100 200 300 400 500 600

4. General description of uniform motion 0 X x = x 0 +vt x0x0 x- x 0 = vt Change in the position is directly proportional to time. Coefficient of proportionality is speed time, s speed, m/s time, s position, m Slope = speed

5. time, s position, m average velocity

6. time, s position, m Slope = instantaneous velocity Instantaneous Velocity

7. Observe and analyze. You place a cart on a smooth metal track tilted at a 10 0 horizontal angle. The data table provides records of the position of the front of the cart at different times. Clock reading t(s)Position x(m) t 0 = 0.00x 0 = 0.00 t 1 = 0.50x 1 = 0.21 t 2 = 1.00x 2 = 0.85 t 3 = 1.50x 3 = 1.91 t 4 = 2.00x 4 = 3.40 t 5 = 2.50x 5 = 5.31 Draw a motion diagram for the cart; consider the cart as a particle. 10 0 x Changing Velocity (homework) Draw a position-versus-clock reading graph for the cart. x, m t, s 0.51.01.52.02.5 0 1 2 3 4 5 6

8. Observe and analyze. You place a cart on a smooth metal track tilted at a 10 0 horizontal angle. The data table provides records of the position of the front of the cart at different times. Clock reading t(s)Position x(m) t 0 = 0.00x 0 = 0.00 t 1 = 0.50x 1 = 0.21 t 2 = 1.00x 2 = 0.85 t 3 = 1.50x 3 = 1.91 t 4 = 2.00x 4 = 3.40 t 5 = 2.50x 5 = 5.31 10 0 x Changing Velocity Calculate the average velocity for the cart for each time interval and complete the table that follows. Time interval  t =t n - t n-1 Displaceme nt  x = x n - x n-1 Average time (t n + t n-1 )/2 Average velocity

9. Observe and analyze. You place a cart on a smooth metal track tilted at a 10 0 horizontal angle. The data table provides records of the position of the front of the cart at different times. 10 0 x Changing Velocity Plot this average velocity on a velocity-versus-time graph. The time coordinate for each average velocity coordinate should be in the middle of the corresponding time interval (the average time for that time interval). Make a best-fit curve for your graph line. Time interval  t =t n - t n-1 Displacement  x = x n - x n-1 Average time (t n + t n-1 )/2 Average velocity, m/s 0.50.210.250.42 0.50.640.751.28 0.51.061.252.12 0.51.491.752.98 0.51.912.253.82 Clock reading t(s)Position x(m) t 0 = 0.00x 0 = 0.00 t 1 = 0.50x 1 = 0.21 t 2 = 1.00x 2 = 0.85 t 3 = 1.50x 3 = 1.91 t 4 = 2.00x 4 = 3.40 t 5 = 2.50x 5 = 5.31

10. Observe and analyze. You place a cart on a smooth metal track tilted at a 10 0 horizontal angle. The data table provides records of the position of the front of the cart at different times. 10 0 x Changing Velocity Plot this average velocity on a velocity-versus-time graph. The time coordinate for each average velocity coordinate should be in the middle of the corresponding time interval (the average time for that time interval). Make a best-fit curve for your graph line. Time interval  t =t n - t n-1 Displacement  x = x n - x n-1 Average time (t n + t n-1 )/2 Average velocity, m/s 0.50.210.250.42 0.50.640.751.28 0.51.061.252.12 0.51.491.752.98 0.51.912.253.82 v, m/s t, s 0.51.01.52.02.5 0 1 2 3 4 5 6

11. Acceleration Speed changes at CONSTANT rate t=0 t=4s v 0 =0m/s v 1 =2m/s v 2 =4m/s v 3 =6m/ s v 4 =8m/ s The rate of change of velocity is ACCELERATION Write a general expression for the velocity as a function of time Time t (s) Velocity v (m/s) t 0 = 0 t 1 = 1 t 2 = 2 t 3 = 3 t 4 = 4 … t v 0 = 0 v 1 = 2 v 2 = 4 v 3 = 6 v 4 = 8 … v t = ? Time t (s) Velocity v (m/s) t 0 = 0 t 1 = 1 t 2 = 2 t 3 = 3 t 4 = 4 … t v 0 = 0 v 1 = 2 v 2 = 4 v 3 = 6 v 4 = 8 … v t = 2×t v = at

12. Acceleration Speed changes with CONSTANT rate Time t (s) Velocity v (m/s) t 0 = 0 t 1 = 1 t 2 = 2 t 3 = 3 t 4 = 4 … t v 0 = 0 v 1 = 2 v 2 = 4 v 3 = 6 v 4 = 8 … v t = 2t v, m/s t, s 12345 0 2 4 6 8 10 12 6 v = at

13. General description of motion with constant acceleration v = v 0 -at v 0 - v = at Change in the velocity is directly proportional to time. Coefficient of proportionality is acceleration time, s acceleration, m/s 2 time, s velocity, m/s Slope = acceleration acceleration = change in velocity time

14. The position of two blocks at successive 0.20-second time intervals are represented by numbered squares in the figure below. The blocks are moving toward the right. Do the blocks ever have the same speed? 1 2 3 45 6 78 1234567 (A) No (B) Yes, at instant 2. (C) Yes, at instant 5. (D) Yes, at instants 2 and 5. (E) Yes, at some time during the interval 3 to 4.

15. Quiz 0 X 640m Find the position and time when the two bikes meet a)Algebraically: Find the position and time using mathematical expressions. b)Graphically: Construct a position-versus-time graph for the two bike trips. 5 m/s 7 m/s