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

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

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

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 Acceleration 1 Diagram Calculation

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

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

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

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

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

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

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

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

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

END of Kinematics 2

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

Kinematics 2 Click Back to Speed and Velocity 3 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 3 m AB 4 m C North 36.9° Back to

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

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

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

Kinematics 2 A paper tape is shown in the following diagram. Click Back to Acceleration 2 2 cm5 cm8 cm ABCD Average velocity (whole path) This is so-called the 2-tick interval. Average velocity (from A to B) Acceleration Average velocity (from C to D) Back to

Kinematics 2 Click Back to Acceleration 2 Cut the following tape according to the dotted lines. velocity time 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 Back to

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

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

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

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

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

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

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

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

Kinematics 2 Click Back to Equations of Motion -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. u = 8 m s -1 v = ? s = ? a = -2 m s -1 t = 6 s Back to

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

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