MEI Conference Preparing to teach motion graphs. Sharon Tripconey.

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1 MEI Conference 2016 Preparing to teach motion graphs Sharon Tripconey 1 of 5 Preparing to teach motion graphs June 2016 MEI

2 Kinematics content extracts for reformed Mathematics A level from Sept 2017 Extracts taken from Mathematics AS and A level content (2014), DfE. Note that bold text within [square brackets] is AS content. P Quantities and units in mechanics Ref P1 Content description [Understand and use fundamental quantities and units in the S.I. system: length, time, mass] [Understand and use derived quantities and units: velocity, acceleration, force, weight], moment Q: Kinematics Ref Q1 Q2 Q3 Q4 Q5 Content description [Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration] [Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph] [Understand, use and derive the formulae for constant acceleration for motion in a straight line]; extend to 2 dimensions using vectors [Use calculus in kinematics for motion in a straight line: v = dr dt, a = dv = d2 r dt dt 2, r = v dt, v = a dt ]; extend to 2 dimensions using vectors Model motion under gravity in a vertical plane using vectors; projectiles 2 of 5 Preparing to teach motion graphs June 2016 MEI

3 velocity displacement 0 time 0 time 3 of 5 Preparing to teach motion graphs June 2016 MEI

4 4 of 5 Preparing to teach motion graphs June 2016 MEI

5 Some useful links: Moving man: Traffic graphs (GeoGebra): MEI s M 4 magazine, Issue 49: Integral resources **NEW** Walkthroughs: Information and professional development: of 5 Preparing to teach motion graphs June 2016 MEI

7 Preparing to teach motion graphs Sharon Tripconey

8 Session description This session is one of four designed to help teachers prepare for teaching mechanics topics in the new A level from Preparing to teach motion graphs will cover some of the basic subject content, links to GCSE and other A level topics, as well as exploring ideas and approaches for teaching this topic. The session will demonstrate how simple practical classroom activities can provide a stimulus for students to develop their understanding of motion graphs. This session is particularly suitable for teachers who have not previously taught any mechanics.

9 position distance travelled

10 Describing quantities Scalar quantity distance distance travelled speed time Vector quantity displacement position velocity acceleration It is not a specific requirement within GCSE Mathematics to know the terms vector and scalar quantities and understand the distinction, but it is in GCSE Science.

11 Mathematics GCSE subject content (DfE) 14 Plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration Awarding organisations may use any flexibility to increase depth, breadth or context within the specified topics or to consolidate teaching of the subject content.

12 Mathematics GCSE subject content (DfE) 15. Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity- time graphs and graphs in financial contexts Awarding organisations may use any flexibility to increase depth, breadth or context within the specified topics or to consolidate teaching of the subject content.

13 Reformed A level Content Mechanics content Q: Kinematics Ref Q1 Q2 Q3 Content description [Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration] [Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph] [Understand, use and derive the formulae for constant acceleration for motion in a straight line]; extend to 2 dimensions using vectors Q4 Q5 Model motion under gravity in a vertical plane using vectors; projectiles

14 Displacement, distance & distance travelled displacement 0 time

15 Displacement, distance & distance travelled distance displacement distance travelled 0 time What is significant about the gradient in these graphs?

16 Displacement & position position displacement 0 time

17 Language of motion Average speed = total distance travelled total time taken Average velocity = total displacement total time taken

18 Displacement & distance travelled displacement distance travelled Average speed = total distance travelled total time taken 0 time Average velocity = total displacement total time taken

19 Velocity and speed velocity 0 time

20 Velocity and speed velocity speed 0 time

21 Comments A distance time graph has less information than a displacement time graph. You cannot deduce displacement from distance travelled. Similarly, you cannot deduce velocity from speed. It is easy to confuse graphs of velocity-time (v t) and displacement-time (y t) with displacement-displacement (y x)

22 Extending basic ideas The instantaneous velocity is the gradient of the displacement time graph displacement s m time t s

23 Acceleration Acceleration is a measure of how much velocity is changing. This means it can affect both the speed and direction of motion. If we only consider motion along a straight line, only two directions are possible, either forwards or backwards. An acceleration of 2 ms -2 means that the velocity of a particle increases by 2 ms -1 every second (by 2 metres per second per second). For example, if a car has an initial velocity of 6 ms -1 and an acceleration of 2 ms -2, then after 1 second its velocity will be 8 ms -1, after 2 seconds 10 ms -1 and after 3 seconds 12 ms -1 etc.

24 Exercise This is a velocity-time graph for the journey of an object moving in a straight line. Describe the motion as fully as you can.

25 Constant velocity = 4m/s (gradient is zero) Area=displacement = = 30m v=0 indicates a change in direction gradient = acceleration +0.8ms -2 Area=displacement = -( ) = -14m gradient = acceleration -1 ms -2 Area 9.5m (approx)

26 Moving Man

27 Acceleration If a particle has a negative acceleration but a positive velocity, then it will slow down to a stop and then move in the opposite direction, with its speed steadily increasing. Take care with the word deceleration. It is probably better not to use it! Use negative accelerations instead. Take care that the units of acceleration are ms -2. This is usually read as metres per second squared, or sometimes as metres per second per second. Accelerations can be found using the gradients of velocity-time graphs.

28 Key features of velocity-time graphs GRADIENT represents acceleration AREA UNDER GRAPH represents displacement

29 Summary Motion Graph Displacement -time Gradient Area Notes Velocity Not significant Velocity-time Acceleration Displacement Accelerationtime Rate of change of acceleration Velocity Vertical axis can be positive or negative Areas below the time axis represent negative displacement. v=0 indicates a possible change in direction

32 About MEI Registered charity committed to improving mathematics education Independent UK curriculum development body We offer continuing professional development courses, provide specialist tuition for students and work with industry to enhance mathematical skills in the workplace We also pioneer the development of innovative teaching and learning resources

#MEIConf2018. Variable Acceleration. Sharon Tripconey

#MEIConf2018. Variable Acceleration. Sharon Tripconey @MEIConference #MEIConf2018 #MEIConf2018 Variable Acceleration Sharon Tripconey #MEIConf2018 Kinematics in A level Maths Ref Q1 Q2 Q3 Q4 Q5 Content description [Understand and use the language of kinematics: