Kinematics 2

1. Speed and Velocity 1 Kinematics 2 Next Slide Speed • Definition : distance traveled per unit time • Unit : metre per second (m s-1) • Nature : scalar (with magnitude only)

2. Speed and Velocity 2 Kinematics 2 Next Slide Velocity • Definition : displacement traveled per unit time • Unit : metre per second (m s-1) • Nature : vector (with magnitude and direction)

3. Speed and Velocity 3 Kinematics 2 Next Slide Concepts of speed and velocity • Daily Use of Terms and Description Photo • Different kinds of motion Difference between speed and velocity • Different descriptions of motions • e.g. small velocity but high speed • Example Calculation

4. Acceleration 1 Kinematics 2 Next Slide Acceleration • Definition : change in velocity per unit time • Unit : metre per second squared (m s-2) • Nature : vector (with magnitude and direction) • Accelerating motion and decelerating motion Diagram Calculation

5. Acceleration 2 Kinematics 2 Next Slide Ticker Timer • Frequency : 50 Hz • Time Duration between 2 dots : 0.02s • Different patterns of dots Diagram • Calculation of velocity/acceleration from dots Calculation • Tape chart Diagram

6. Acceleration 3 Kinematics 2 Next Slide Stroboscope • Frequency depends on the machine • Time Duration between 2 images : calculated from the frequency • Calculation of speed/velocity/acceleration from images Calculation

7. Time Graphs 1 Kinematics 2 Next Slide Time graphs • Three different kinds of time-graphs • Linear motions only • Direction shown by the sign of the data • Displacement vs time graphs (s vs t graphs) • Velocity vs time graphs (v vs t graphs) • Acceleration vs time graphs (a vs t graphs)

8. Time Graphs 2 Kinematics 2 Next Slide Displacement vs time graphs • Constant displacement situation • Constant velocity situation • Constant acceleration situation • The graphs’ slope and velocity Graph

9. Time Graphs 3 Kinematics 2 Next Slide Velocity vs time graphs • Constant displacement situation • Constant velocity situation • Constant acceleration situation • The graphs’ slope and acceleration Graph • The graphs’ area and displacement Graph

10. Time Graphs 4 Kinematics 2 Next Slide Acceleration vs time graphs • Constant displacement situation • Constant velocity situation • Constant acceleration situation • The graphs’ area and change in velocity Graph

11. Equations of Motion 1 Kinematics 2 Next Slide Equations of motion • Linear motions only • Constant acceleration situation only • Direction given by the signs of the values • Introduction of parameters involved Diagram

12. Equations of Motion 2 Kinematics 2 Next Slide Equations of motion • Example 1 Calculation • Example 2 Calculation • Example 3 (Turning point) Calculation

13. Equations of Motion 3 Kinematics 2 Next Slide Projectile motion • Acceleration due to gravity (g) = 10 m s-2 • It is always pointing downwards • Projectile Motion Calculation • Example Calculation

14. END of Kinematics 2

15. Back to Speed and Velocity 3 Kinematics 2 Click Back to Different kinds of motion Constant speed (slow) Constant speed (fast) Moving slower and slower Moving faster and faster

16. C North 36.9° 4 m A B 3 m Back to Speed and Velocity 3 Kinematics 2 Click Back to Consider the motion of the person in the following diagram. He takes 6 seconds to travel 3 m due east from A to B. He takes 4 seconds to travel 4 m due north from B to C. Average speed from A to C Average velocity from A to C

17. Back to Acceleration 1 Kinematics 2 Click Back to Accelerating motion Decelerating motion

18. 2 m s-1 6 m s-1 Back to Acceleration 1 Kinematics 2 Click Back to An object changes its velocity from 2 m s-1 to 6 m s-1 in 4 seconds. What is its acceleration?

19. Starting point Back to Acceleration 2 Kinematics 2 Click Back to Different pattern of dots Small constant velocity Large constant velocity Accelerating motion Decelerating motion

20. 2 cm 5 cm 8 cm A B C D Back to Acceleration 2 Kinematics 2 Click Back to A paper tape is shown in the following diagram. Average velocity (from A to B) Average velocity (from C to D) Acceleration Average velocity (whole path) This is so-called the 2-tick interval.

21. Cut the following tape according to the dotted lines. Back to Acceleration 2 Kinematics 2 Click Back to velocity Arrange the tapes (2-tick interval) side by side Join the top of each tape Add x-axis (time) and y-axis (velocity) Suitable scale should be chosen for x-axis (time) and y-axis (velocity) We can choose different intervals time

22. The images of an object sliding down an inclined plane : A B Frequency of stroboscope = 10 Hz C D 2 cm 5 cm E 8 cm 11 cm Back to Acceleration 3 Kinematics 2 Click Back to Time between successive images Average velocity (from A to B) Average velocity (from C to D) Acceleration

23. s (m) s (m) s (m) 4 3 t(s) t (s) t (s) 2 2 0 0 Back to Time Graphs 2 Kinematics 2 Click Back to Slope = 0 Velocity = 0 m s-1 Slope = 2 Velocity = 2 m s-1 Constant displacement Constant velocity Slope is increasing Velocity is increasing Slope of s-t graph = Velocity at that time Constant acceleration

24. v (m s-1) v(m s-1) v(m s-1) 4 t (s) t (s) t (s) 2 2 0 0 4 2 Back to Time Graphs 3 Kinematics 2 Click Back to Slope = 0 Acceleration = 0 m s-2 Slope = 0 Acceleration = 0 m s-2 Constant displacement Constant velocity Slope = 2 Acceleration = 0 m s-2 Slope of v-t graph =Acceleration at that time Constant acceleration

25. v (m s-1) v(m s-1) v (m s-1) 4 t(s) t (s) t (s) 2 2 0 0 4 2 0 Back to Time Graphs 3 Kinematics 2 Click Back to Area = 0 Displacement traveled = 0 m Area = 8 Displacement traveled = 8 m Constant displacement Constant velocity Area = 8 Displacement traveled = 4 m Area of v-t graph = Displacement traveled Constant acceleration

26. a (m s-2) a(m s-2) a(m s-2) t(s) t (s) t (s) 2 2 0 0 4 2 0 Back to Time Graphs 4 Kinematics 2 Click Back to Area = 0 Change in velocity = 0 m s-1 Area = 0 Change in velocity = 0 m s-1 Constant displacement Constant velocity Area = 8 Change in velocity = 8 m s-1 Area of a-t graph = Change in velocity Constant acceleration

27. u = initial velocity v = initial velocity a = acceleration s = displacement traveled t = time required Kinematics 2 Back to Equations of Motion 1 Click Back to Equations of Motion : (take forward direction as +ve)

28. u = 2 m s-1 v = 8 m s-1 a = ? s = ? t = 4 sec Back to Equations of Motion 2 Kinematics 2 Click Back to +ve acceleration means the object is accelerating +ve displacement means forward displacement

29. u = 8 m s-1 v = 2 m s-1 a = ? s = 10 m t = ? Back to Equations of Motion 2 Kinematics 2 Click Back to -ve acceleration means the object is decelerating

30. u = 8 m s-1 v = ? a = -2 m s-1 s = ? t = 6 s Back to Equations of Motion Kinematics 2 Click Back to -ve final velocity means the object is moving backwards at that time. Where is the “turning point”? At t = 4 s, the object stops momentarily.

31. a = -10 m s-2 -ve acceleration means it is pointing downwards (upward direction) Back to Equations of Motion 3 Kinematics 2 Click Back to

32. v = 10 m s-1 a = -10 m s-2 -ve acceleration means it is pointing downwards (upward direction) s = ? t = ? u = 50 m s-1 Back to Equations of Motion 3 Kinematics 2 Click Back to +ve displacement means upward displacement