Definition : distance traveled per unit time 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)

Definition : displacement traveled per unit time 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)

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

Definition : change in velocity per unit time 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

Time Duration between 2 dots : 0.02s 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

Frequency depends on the machine 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

Three different kinds of time-graphs 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)

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

Velocity vs time graphs 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

Acceleration vs time graphs 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

Constant acceleration situation only 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

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

Acceleration due to gravity (g) = 10 m s-2 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

END of Kinematics 2

Different kinds of motion 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

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. 4 m C Average speed from A to C North 36.9° Average velocity from A to C 3 m A B

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

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? 2 m s-1 6 m s-1

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

Back to Acceleration 2 Kinematics 2 Click Back to A B C D A paper tape is shown in the following diagram. 2 cm 5 cm 8 cm A B C D 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.

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

Back to Acceleration 3 Kinematics 2 Click Back to A B C D E 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) Acceleration

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

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

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

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

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

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

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

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

Back to Equations of Motion 3 Kinematics 2 Click Back to 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 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) +ve displacement means upward displacement