2.1+Kinematics

=Learning outcomes= New Syllabus

toc

=Distance and displacement=

@http://www.absorblearning.com/media/attachment.action?quick=4n&att=326

@http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/DisplaceDistance/DisplaceDistance.html

=Instantaneous and average velocity= @http://webphysics.davidson.edu/physlet_resources/physlet_physics/contents/mechanics/one_d_kinematics/illustration2_3.html



Definitions Some important definitions are shown in the table below: || **Quantity** || **Symbol** || **Definition** || **Example** || **SI Unit** || **Vector or Scalar** ||
 * 8.4.1 - Kinematics (motion in a straight line) ||
 * [|definitions] / [|instantaneous and average velocity]
 * Displacement || s or r || The distance moved in a particular direction. || The displacement from London to Rome is 1.43 x 106 m southeast. || m || vector ||
 * Velocity || v or u || The rate or change of displacement

|| The average velocity during a flight from London to Rome is 160 ms-1southeast. || ms-1 || vector ||
 * Speed || v or u || The rate of change of distance.

|| The average speed during a flight from London to Rome is 160 ms-1. || ms-1 || scalar || || The average acceleration of a plane on the runway during take-off is 3.5 ms-2 in a forwards direction. This means that on average, its velocity changes every second by 3.5 ms-1. || ms-2 || vector || These technical terms should not be confused with their everyday use. In particular you should note that: Instantaneous and Average Velocity The average value of velocity over a period of time is very different to the instantaneous value at a particular instant in time. Imagine a sprinter during a 100 m race where the sprinter covered the distance in 11.3 seconds. The average speed over the whole race is easy to work out. It is the total distance (100 m) divided by the time (11.3 s) giving 8.5 ms-1. During the race, however, her instantaneous speed would have changed. If at the end of 2.0 seconds she had travelled 10.4 m, here average speed for the first two seconds would have been 10.04/2.0 = 5.0 ms-1. During these first two seconds her instantaneous speed was increasing - she was accelerating. If she started at rest and her average speed over the whole 2 s was 5.02 ms-1 then her instantaneous speed at 2 s must be more than this. In fact, the instantaneous speed for this sprinter was 9.23 ms-1 at 2 s, but it would have been impossible to work this out from the information given. You can use the following website to see an animation showing the difference between average speed and instantaneous speed. []
 * Acceleration || a || The rate of change of velocity.
 * vector quantities always have a direction associated with them.
 * generally, velocity and speed are NOT the same thing. This is particularly important if the object is not going in a straight line.

=Constant velocity= @http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/MotionDiagram/MotionDiagram.html

=Constant acceleration= @http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/ConstantAccel/ConstantAccel.html =Kinematics - important web resources=

esson 1 : Describing Motion with Words

 * 1) [|Introduction to the Language of Kinematics]
 * 2) [|Scalars and Vectors]
 * 3) [|Distance and Displacement]
 * 4) [|Speed and Velocity]
 * 5) [|Acceleration]

Lesson 2 : Describing Motion with Diagrams

 * 1) [|Introduction to Diagrams]
 * 2) [|Ticker Tape Diagrams]
 * 3) [|Vector Diagrams]

Lesson 3 : Describing Motion with Position vs. Time Graphs

 * 1) [|The Meaning of Shape for a p-t Graph]
 * 2) [|The Meaning of Slope for a p-t Graph]
 * 3) [|Determining the Slope on a p-t Graph]

Lesson 4 : Describing Motion with Velocity vs. Time Graphs

 * 1) [|The Meaning of Shape for a v-t Graph]
 * 2) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|The Meaning of Slope for a v-t Graph]
 * 3) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Relating the Shape to the Motion]
 * 4) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Determining the Slope on a v-t Graph]
 * 5) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Determining the Area on a v-t Graph]

<span style="background-color: #ffffff; color: #0099cc; font-family: Verdana,Geneva,Arial,Helvetica,sans-serif; font-size: 14px;">Lesson 5 : Free Fall and the Acceleration of Gravity

 * 1) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Introduction to Free Fall]
 * 2) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|The Acceleration of Gravity]
 * 3) <span style="background-color: #ffffff; color: #ff6600; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-decoration: none;">[|Representing Free Fall by Graphs]
 * 4) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|How Fast? and How Far?]
 * 5) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|The Big Misconception]

<span style="background-color: #ffffff; color: #0099cc; font-family: Verdana,Geneva,Arial,Helvetica,sans-serif; font-size: 14px;">Lesson 6 : Describing Motion with Equations

 * 1) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|The Kinematic Equations]
 * 2) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Kinematic Equations and Problem-Solving]
 * 3) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Kinematic Equations and Free Fall]
 * 4) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Sample Problems and Solutions]
 * 5) <span style="background-color: #ffffff; color: #980000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">[|Kinematic Equations and Graphs]

= Kinematics and displacement-time graphs – background material for Physclips = <span style="background-color: #ffffff; font-family: 'Times New Roman'; font-size: medium; text-align: -webkit-left;">Displacement-time graphs are used in kinematics, the quantitative study of motion. In kinematics, the motion is quanified, but not explained: forces, energy and momenta come later. This page presents some supporting material for the multimedia tutorial about constant acceleration from Physclips.
 * <span style="background-color: #ffffff; font-family: 'Times New Roman'; font-size: medium; text-align: -webkit-left;">[|Constant velocity]
 * <span style="background-color: #ffffff; font-family: 'Times New Roman'; font-size: medium; text-align: -webkit-left;">[|Constant acceleration]


 * [[image:http://www.animations.physics.unsw.edu.au/images/download_acceleration1.gif width="334" height="251" link="@http://www.animations.physics.unsw.edu.au/jw/calculus.htm#differentiation"]] || [[image:http://www.animations.physics.unsw.edu.au/images/download_acceleration2.gif width="334" height="251" link="@http://www.animations.physics.unsw.edu.au/jw/calculus.htm#varying"]] ||
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">[|Download (.zip)] || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">[|Download (.zip)] ||

=Exploring motion with graphs=

Visit @http://physics-online.com/app/ Under Topic 2 Mechanics visit the section on displacement- time graph. An interesting way of setting the graphs and then observing the motion.





=Derivation of equations of motion= <span style="background-color: #f7f7f8; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 24px; text-align: left;">Derivations of Equations of Motion (Graphically) <span style="background-color: #f7f7f8; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 24px; text-align: left;">First Equation of Motion <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Graphical Derivation of First Equation <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Consider an object moving with a uniform velocity u in a straight line. Let it be given a uniform acceleration a at time t = 0 when its initial velocity is u. As a result of the acceleration, its velocity increases to v (final velocity) in time t and S is the distance covered by the object in time t. <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">The figure shows the velocity-time graph of the motion of the object. <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Slope of the v - t graph gives the acceleration of the moving object. <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Thus, acceleration = slope = AB = <span style="background-color: #f7f7f8; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 16px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">v - u = at <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">v = u + at **I equation of motion** <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Graphical Derivation of Second Equation <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Distance travelled S = area of the trapezium ABDO <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">= area of rectangle ACDO + area of D ABC <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">(v = u + at I eqn of motion; v - u = at) <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 16px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Graphical Derivation of Third Equation <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">S = area of the trapezium OABD. <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">Substituting the value of t in equation (1) we get, <span style="background-color: #f7f7f8; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 16px; text-align: left;"> <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">2aS = (v + u) (v - u) <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">(v + u)(v - u) = 2aS [using the identity a 2 - b 2 = (a+b) (a-b)] <span style="background-color: #f7f7f8; display: block; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">v 2 - u 2 = 2aS **III Equation of Motion** =Acceleration due to gravity and falling bodies=

From the top of a tower
@http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/FluidDynamics/BallCNTower/BallCNTower.html

Ball with or without air resistance
@http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

**Physics behind sky diving**

 * Go to the link @http://www.waowen.screaming.net/revision/force&motion/skydiver.htm**

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Saving the parachuter
@http://www.physics4me.com/launch_sim.php?sid=2



Investigating drag forces
@http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/FluidDynamics/ViscousMotion/ViscousMotion.html



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