POSITION-TIME GRAPHS &

SPEED-TIME GRAPHSYEAR 12

UNIT 1

MODULE 1

LESSON 5

UNIFORM VELOCITY - CONSTANT

•REMINDER

•VELOCITY = DISPLACEMENT / TIME

•V = S/T

•THEREFORE

•DISPLACEMENT = VELOCITY X TIME

•S= V T

UNIFORM VELOCITY - CONSTANT

•REMINDER

•ACCELERATION = CHANGE IN VELOCITY / TIME

•A=(V-U)/T

•THEREFORE

•V=U+AT

UNIFORM VELOCITY - CONSTANT

•REMINDER

•ALSO, REMEMBER INSTANTANEOUS AND AVERAGE VELOCITIES

•AND DIFFERENCES BETWEEN DISPLACEMENT AND DISTANCE

Draw a set of axes. Time in seconds along the x-axis. Displacement in metres up the y-axis. Draw up to 10 on both axes.

• DRAW THE FOLLOWING: A LINE ON THE GRAPH TO REPRESENT:

• A) STOOD STILL AT POSITION, 0M

• B) STOOD STILL AT 3M

• C) WALKING STEADILY AT 1M/S, STARTING AT POSITION 0M

• D) WALKING STEADILY AT 4M/S, STARTING AT POSITION 2M

• E) ACCELERATING WHILST WALKING FORWARD

(DON’T WORRY ABOUT NUMBERS, JUST SHOW ME THE RIGHT SHAPE OF LINE)

• F) DECELERATING WHILST WALKING FORWARD

• G) STARTING AT 10M AND WALKING AT 2M/S BACK TO THE START POINT (0M)

• H) WALKING FORWARDS AT 2M/S FOR 3 SECONDS, AND THEN STANDING STILL FOR 4 SECONDS, BEFORE RUNNING BACK TO THE START POINT (0M) AT 6M/S

• ON YOUR PAPER (AS OPPOSE TO WHITEBOARDS), TRY TO DRAW ALL THE SEPARATE LINE ELEMENTS FOR A DISPLACEMENT-TIME GRAPH

• E.G. STEADY POSITIVE VELOCITY

A few of the possible lines on a displacement – time graph. Can you think of any others?

EACH TYPE OF MOTION ON A DISPLACEMENT-TIME GRAPH

• SLIDE COMING SOON, TO A WHIEBOARD NEAR YOU!

• (PROBABLY JUST WANT TO WRITE THEM DOWN FOR NOW)

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DISCUSS IN PAIRS, WRITE YOUR ANSWER ON YOUR WHITEBOARDS:

• WHAT WOULD LOOK DIFFERENT ON A DISPLACEMENT-TIME GRAPH TO A DISTANCE-TIME GRAPH?

• NEGATIVE DISPLACEMENT. (I.E. MOVING BACK TOWARDS WHERE YOU STARTED), TECHNICALLY SPEAKING, ON A DISTANCE-TIME GRAPH, YOU CANNOT HAVE A NEGATIVE DISTANCE, AS DISTANCE IS A SCALAR.

• TAYA WALKS A STEADY VELOCITY FOR 15 SECONDS, FOR 60M

• SHE THEN STAYS STATIONARY FOR 20 SECONDS

• AND THEN WALKS A STEADY VELOCITY FOR 5 MORE SECOND, FOR 10M

• SHE THEN RETURNS THE 70M HOME OVER 60 SECONDS, BY WALKING AT A STEADY SPEED

• DRAW THIS DISPLACEMENT-TIME GRAPH

• HOW CAN YOU FIND TAYA’S VELOCITY AT A GIVEN POINT IN HER JOURNEY FROM THIS GRAPH?

THE GRADIENT OF DISPLACEMENT-TIME GRAPH IS VELOCITY!!!!!!!!!!!!!!!!!

BECAUSE:

GRADIENT = CHANGE IN Y / CHANGE IN X

= CHANGE IN DISPLACEMENT / CHANGE IN TIME

= CHANGE IN VELOCITY

WHAT WOULD THE GRADIENT OF A DISTANCE-TIME GRAPH BE?

• -GO THROUGH MOTION GRAPH QUESTION ON BASELINE TEST

EXAM QUESTIONS

ANSWERS

WALKING DISPLACEMENT-TIME GRAPHS

SPEED-TIME & VELOCITY-TIME GRAPHS

LOOK AT ALL YOUR POSSIBLE LINES FROM DISPLACEMENT-TIME GRAPH.

• WHAT WOULD THEY LOOK LIKE ON A VELOCITY-TIME GRAPH?

• CAN YOU ADD ANY MORE LINES?

EACH TYPE OF MOTION ON A VELOCITY-TIME GRAPH

• SLIDE COMING SOON, TO A WHIEBOARD NEAR YOU!

• (PROBABLY JUST WANT TO WRITE THEM DOWN FOR NOW)

• (ALMOST AS MUCH OF AN ANTI-CLIMAX AS THE FIRST TIME I SHOWED THIS SLIDE)

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Template copyright www.brainybetty.com 2005 2815/09/06

•

•Draw a displacement –time graph for bob’s journey. Distance should be along the y-axis, and time on the x-axis

•Bob is out for a walk. He starts travelling at 0.5m/s for 20 secs• He then jogs on for 10 secs at a speed of 5m/s• He then stops for 10 seconds to remember what he forgot but can't.• He suddenly remembers what it was and walks back at for 20 secs at 3m/s

• DRAW THE SPEED-TIME GRAPH FOR BOB’S JOURNEY

• WHAT DOES THE GRADIENT OF THIS GRAPH TELL US ABOUT A GIVEN PARTO F HIS JOURNEY?

• HOW CAN WE FIND THE DISTANCE TRAVELLED FROM THIS GRAPH?

• GRADIENT OF A VELOCITY-TIME GRAPH IS ACCELERATION

• AREA UNDERNEATH THE GRAPH IS DISTANCE TRAVELLED

SPEED-TIME GRAPHS IN TERMINATOR 2(ONE OF THE TERMINATOR FILMS THAT

DIDN’T SUCK… I’M LOOKING AT YOU TERMINATOR 3)

• HTTP://WWW.YOUTUBE.COM/WATCH?V=4DERTTFCTB4

• RECORD THE TIME THAT EACH FO THE EVENTS HAPPEN IN THE CHASE AND FIL LTHEM IN ON THE SHEET. FROM HERE WE CAN PLOT A SPEED-TIME GRAPH

HOMEWORK

EXTRA SLIDES

• ADD HOMEWORK

• ADD EXAM QUESTIONS

• SORT OUT PICTURES OF ALL LINE ELEMENT SLIDES

• GATHER RESOURCES E.G. TERMINATOR ONES

• HOW CAN WE WORK OUT VELOCITY FROM A DISPLACEMENT-TIME GRAPH?

• VELOCITY IS RATE OF CHANGE OF POSITION.

• WE NEED TO FIND OUT HOW RAPIDLY THE POSITION IS CHANGING

• OUR GRAPH LETS US DO THIS EASILY – IT’S SIMPLY THE GRADIENT!!!

• WHAT ABOUT DISTANCE-TIME GRAPHS?

• CAN WE HAVE A NEGATIVE VALUE ON A DISTANCE-TIME GRAPH?

• NO – DISTANCE IS JUST THE PATH TAKEN, IT HAD NO DIRECTION, HENCE NEGATIVE DISTANCE DOESN’T REALLY MEAN ANYTHING

• WHAT WOULD THE GRADIENT OF A DISTANCE-TIME GRAPH BE?

• SPEED, SPEED = DISTANCE/TIME

• WRITE 3 QUESTIONS ON A PIECE OF PAPER. ANYTHING FROM THIS LESSON…