Motion Graphs

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# Motion Graphs - PowerPoint PPT Presentation

Motion Graphs. Distance and Displacement. Distance is a scalar quantity! is how far something has moved. is measured in metres etc. Displacement is a vector quantity. is how far an object has moved from its starting point and in what direction.

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## PowerPoint Slideshow about 'Motion Graphs' - savea

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Presentation Transcript

### Motion Graphs

Distance

and

Displacement

Distance

• is a scalar quantity!
• is how far something has moved.
• is measured in metres etc.
• Displacement
• is a vector quantity.
• is how far an object has moved from its starting point and in what direction.
• measured in metres but also has a direction.
• is the (straight line) distance between 2 points with the direction given too!

If the bear skis the 7 metres to the tree then back to the start and then all the way to the house, what distance would he have gone? _______m

What would his displacement from the starting point be ? ___________ m in an easterly direction.

Speed

and

velocity

Speed is a scalar quantity!

• It is how fast something has travelled
• It is measured in metres/second or km/hour.
• Velocity is a vector quantity.
• This is how fast and in what direction something travels IN A STRAIGHT LINE!!!
• This is measured in m/s or km/h but also has a direction.

Speed

• If a car travels 150 km in 2 hours then calculate the average speed of the car:

Average Speed = distance travelled/ time

= d/t

= 150 km/ 2 h

= 75km/h

Or write it like this:

= 75 km h ⁻¹

Velocity

• If a plane travels 480 km in a southerly direction for 2 hours then calculate the average velocity of the plane:

Average velocity= distance travelled in a straight line time

Vav = s/t

= 480 km/ 2 h South

= 240km/h South

Or write it like this:

= 240 km h ⁻¹ South

Remember that if an object is going at a constant speed but changes direction (turns) then its velocity changes!!

All these abbreviations – what do they stand for???!!!

d = distance

s = displacement

t = time

v= velocity or final velocity

u = initial velocity

a = acceleration

Motion graphs

It is often easier to show the motion of an object with a graph rather than with words.

There are 2 types of graph we will look at:

• Displacement – time graphs or distance – time graphs.
• velocity - time graphs or speed- time graphs.

VELOCITY (v)is simply speed in a given direction

DISPLACEMENT (s) is the distance in a given direction

With both types of graph, time is plotted on the x axis.

• The further to the right along the x axis we go – the longer the time from the start!
• Velocity, distance etc are always plotted on the y axis.
• We assume the initial direction of motion to be positive.

Distance (m)

0 1 2 3 4 5 6 7 8 9 10 11

A body at rest.

That is it is stopped or standing still!

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

An object moving at constant speed.

Constant speed because the lines are straight!

Which line shows the object going fastest?

Distance (m)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Speed is given in m/s so we can work out the speed here by saying speed = rise/run = distance/time.

Work it out for each.

Distance (m)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

A body accelerating!

You can see that the speed is increasing: the distance travelled is more each second so this shows it is accelerating!!

Distance (m)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Lets look at an example:

First we will give the information in words then as a

displacement – time graph.

Matthew starts from point A and travels at 2m/s for 3 seconds to point B. He then stops at point B for 4 seconds before going back towards point A at an initial velocity of -1.5m/s for 2 seconds then stopping at an intersection for 1 second before continuing to point A at -1.5 m/s.

Ok – lets look at this graphically!!!!!

Much Easier than words!!!

Distance (m)

0 1 2 3 4 5 6 7 8 9 10 11

Matthew’s trip

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Lets do

some questions!

This axis has SPEED not distance on it!!!!

What is the difference between this graph and the ones we looked at before??

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

So what does this graph show?

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

It shows that the object is moving at a constant speed of 5.5m/s

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

What does this graph show?

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

It shows that the objects’ speed is increasing or the object is accelerating!

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

What does this graph show?

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

It shows that the objects’ speed is decreasing or the object is decelerating!

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Which line shows faster acceleration? Green or blue?

Acceleration = speed/time so

Blue = 3m/s/s

Green = 1m/s/s

Steeper slope = faster acceleration!

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Putting it all together:

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

Fast deceleration

Or

negative acceleration

Fast accn

Slow accn

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

What other information can we get from displacement – time and speed time graphs?

Speed (m/s)

1 2 3 4 5 6 7 8

Distance (m)

10 20 30 40 50 60

1 2 3 4 5 6 7 8 9 Time (s)

1 2 3 4 5 6 7 8 9 Time (s)

Gradient = rise/run = 7/7 = 1m/s/s = acceleration!!! Area under the graph = ½ time x speed

= s x m/s

= m

= distance travelled!!!

= 30/6

= 5m/s

= speed!

Speed (m/s)

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9 10 11 12 time (s)

Reading – Pages 3 to 4

Can you stick the sheet in too?