1 of 5 Preparing to teach motion graphs June 2016 © MEI

MEI Conference 2016

Preparing to teach motion

graphs

Sharon Tripconey sharon.tripconey@mei.org.uk

2 of 5 Preparing to teach motion graphs June 2016 © MEI

Kinematics content extracts for reformed Mathematics A level from Sept 2017

Extracts taken from ‘Mathematics AS and A level content’ (2014), DfE.

www.gov.uk/government/publications/gce-as-and-a-level-mathematics

Note that bold text within [square brackets] is AS content.

P Quantities and units in mechanics

Ref Content description

P1 [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 Content description

Q1 [Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration]

Q2 [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]

Q3 [Understand, use and derive the formulae for constant acceleration for motion in a straight line]; extend to 2 dimensions using vectors

Q4 [Use calculus in kinematics for motion in a straight line: 𝒗 =𝒅𝒓

𝒅𝒕,

𝒂 =𝒅𝒗

𝒅𝒕=

𝒅𝟐𝒓

𝒅𝒕𝟐, 𝒓 = ∫𝒗𝒅𝒕, 𝒗 = ∫𝒂𝒅𝒕 ]; extend to 2 dimensions using vectors

Q5 Model motion under gravity in a vertical plane using vectors; projectiles

3 of 5 Preparing to teach motion graphs June 2016 © MEI

time 0

velo

city

0

time

dis

pla

cem

en

t

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

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

Some useful links:

Moving man:

https://phet.colorado.edu/en/simulation/moving-man

Traffic graphs (GeoGebra):

http://www.geogebra.org/m/2832353

MEI’s M4 magazine, Issue 49:

http://mei.org.uk/files/pdf/Sept-Oct-2015-1.pdf

Integral resources **NEW** Walkthroughs:

http://integralmaths.org/walkthroughs/index.php?wt=vel_time_graphs

http://integralmaths.org/walkthroughs/?wt=vuat

http://integralmaths.org/walkthroughs/?wt=disp_const_acc

http://integralmaths.org/walkthroughs/index.php?wt=disp_time_graphs

Information and professional development:

http://www.mei.org.uk/2017-pd

http://www.furthermaths.org.uk/teaching-mechanics

http://www.mei.org.uk/files/pdf/mechanics-get-set-course-outline.pdf

Preparing to teach motion

graphs

Sharon Tripconey

Session descriptionThis session is one of four designed to help teachers prepare for teaching

mechanics topics in the new A level from 2017.

‘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.

position

distance travelled

Describing quantities

Scalar quantity Vector quantity

distance displacement

distance travelled position

speed velocity

time 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.

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.”

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.”

Mathematics GCSE subject content (DfE)

Ref Content description

Q1 [Understand and use the language of kinematics: position; displacement;

distance travelled; velocity; speed; acceleration]

Q2 [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]

Q3 [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

Mechanics content

Q: Kinematics

Reformed A level Content

www.gov.uk/government/publications/gce-as-and-a-level-mathematics

Displacement, distance &

distance travelled

time0

displacement

time

displacement

distance travelled

0

What is

significant

about the

gradient in

these

graphs?

distance

Displacement, distance &

distance travelled

Displacement & position

time0

displacement

position

Language of motion

Average speed = total distance travelled

total time taken

Average velocity = total displacement

total time taken

Displacement & distance travelled

Average speed = total distance travelled

total time taken

time

displacement

distance travelled

0

Average velocity = total displacement

total time taken

Velocity and speed

time

velocity

0

Velocity and speed

time

velocity

speed

0

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)

Extending basic ideasThe instantaneous velocity is the gradient of the

displacement – time graph

time 0

displacement

5

5 t s

s m

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.

Acceleration

Describe the motion as fully as you can.

Exercise This is a velocity-time graph for the journey of an object

moving in a straight line.

gradient = acceleration

+0.8ms-2

gradient = acceleration

-1 ms-2

Area=displacement

= -(4.5+9.5) = -14m

Area 9.5m

(approx)

Constant velocity =

4m/s (gradient is

zero)Area=displacement

= 10+12+8 = 30mv=0 indicates a

change in

direction

Moving Man

https://phet.colorado.edu/en/simulation/moving-man

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.

Acceleration

Key features of velocity-time

graphs

• GRADIENT represents acceleration

• AREA UNDER GRAPH represents displacement

Summary

Motion

GraphGradient Area Notes

Displacement

-timeVelocity Not significant

Vertical axis can

be positive or

negative

Velocity-time Acceleration Displacement

Areas below the

time axis

represent negative

displacement. v=0

indicates a

possible change

in direction

Acceleration-

time

Rate of change of

accelerationVelocity

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