Velocity ok

POSITION, DISTANCE, & DISPLACEMENT

AVERAGE SPEED AND VELOCITY

INSTANTANEOUS VELOCITY

By Chaiporn Pattanajak

CHAPTER 2

Line Motion (one Dimension Motion)

It is a change in the position of an object with respect to time.

Section I :POSITION, DISTANCE & DISPLACEMENT

Straight

Let’s look the picture

Introduce•MotionMotion is a change of position or displacement of an object within a certain time interval

Let’s look the picture

Old position

Let’s look the picture

Old positionNew position

New position

A

B

Can you tell me about rockets A and rockets B!

Old position

Let’s look the picture

Old positionNew position

New position

A

BWe can say, rocket A moving and B No !

Moving object is identified by its change of position from a certain point of reference

A change of position or displacement of an object from a certain point of reference is called MOTIONMOTION

Frame of reference (กรอบอ�างอ�ง)Definition : A frame of reference is an extended

Object whose parts are at rest relative to each other.

Frame of reference

Initial Position Final Position

•Displacement is a vector and so must have a distance value andand a a direction. direction. Vector Vector quantity.quantity.

•Distance just has a value. Scalar quantity

Start Point

Finish Point

A

B

(Initial Position)

(Final Position)

• Set up a coordinate system –Right is usually positive, left is usually

negative

– Distance = total length of travel

– Displacement = change in position = final position – initial position or ∆x = xf - xi

• Displacement can be positive, negative, or zero

• What is your distance traveled if you start at your friend’s house travel to the grocery store then back to your house?

• What is your displacement for the same route?

• What are some routes that you could take to have a negative displacement?

• How about a displacement of zero?

In this section you are able to :1. Making a graph of displacement vs

time

2. Finding the equation of speed

3. Identifying the application of constant straight motion in daily life

Section II :

• Average Speed and Velocity

Speed is scalar quantity.(Blue curve)

time

cedisv

tan

Unit : m/s

Velocity is vector quantity. (Green line)

time

ntdisplacemev

Unit : m/st

x

tt

xxv

if

if

t

x

tt

xxv

if

if

ix

fx

• Point of referent is location which is considered fixed (at rest) and used to compare the initial and final position.

• To understand how fast the object moves we have to know time needed to travel the distance of displacement.

Base on component that contents of quantities, quantities can be derived in two kind :

1.Vector (velocity) 2.Scalar (speed)

VelocityFor example1.If some one walking 5

km/hour toward east :a. his speed is 5 km/hourb. his velocity is 5 km/hour to east.

Average Speed and Velocity

• Average speed = distance/elapsed time

Average Speed and Velocity Con’t.• Average velocity = displacement/elapsed

time • Sign tells the direction of the object motion

– + sign means xf > xi

– – sign means xf < xi

Instantaneous Velocity Average velocity isn’t very descriptive about the

exact rate of motion of an object at a specific time Ideally you would calculate the average velocity for

every minute or second Instantaneous velocity, v = – When the velocity is constant, average velocity over any

time interval = instantaneous velocity at any time– When the velocity changes, the instantaneous velocity at

a given time is equal to the slope of the tangent line at that point on a displacement vs. time graph

Graphical Interpretation of Average Velocity

Slope of a line connecting two points on an displacement vs. time plot is equal to the average velocity during that time interval

distance distance (m)(m)

time (s)time (s)

d1d1 t1t1

d2d2 t2t2

GraphGraph

d (m)d2

d1

0 t1 t2 t (s)

VelocityVelocity

Handout

d (m)d2

d1

0 t1 t2 t (s)

GrahpGrahp

Constt

d

t

d

2

2

1

1

VelocityVelocity

This Constant is Called

Velocity

When drawing graphs, follow these steps:

• Decide what data goes on the x-axis and what data goes on the y-axis.

• Title your graph and label the axes, remember to include units.

• Have even scales on your axes. (i.e. 1, 2, 3, 4 … not 1, 2, 5, 8 …)

• Plot your points on the graph. Make sure to start at 0.

• Connect points with a ruler for distance-time and speed-time graphs.

Draw a graph using this data.Copy

You have to be able to describe You have to be able to describe what is happening in a distance-what is happening in a distance-time graph…time graph…

Handout

1. The vehicle covered 100km in the first two hours.

2. The vehicle was stationary between 2 hours and 5 hours.

3. Between 5 hours and 8 hours the vehicle covered a further 180 km.

4. Between 8 hours and 11 hours, the vehicle was stationary.

VelocityVelocity is the change of position within a time interval

If distance (d), time interval (t) and velocity (v), we can write formula of velocity t

dv

The relationship among d, t, and v

t

dv

v

dt

tvd .

d

v t

Calculating the velocityAverage speed is the total

traveled distance divided by the time needed to travel that distance.

t

dv

v = average speedd = total distancet = time total

•We can use the slopeslope of a distance – time graphs to find the speed of an object.

•To do this the graph line must be straight.straight.

t

xSlope

Copy

Slope = velocity

Handout

Calculate the slopeslope for each Car

•The average speed of Car A =•The average speed of Car B =•The average speed of Car C =

Time (h) Speedometer Car A (kmh-1)

0 50

0.5 50

1.0 50

1.5 50

2.0 50

2.5 50

3.0 50

3.5 50

4.0 50

Copy

•Plot a speed – time graph using this data for Car A.

Speed (kmh-1)

Time (s)

Speedometer Car B (kmh-1)

80

80

80

0

0

0

80

80

80

• Just add another column to the table you have already drawn.

Copy

•Just add the Car B data to the graph you already have.

•You will need to make the Car B line different to the Car A line.

•Use two colours or crosses and dots.

Speedometer Car C (kmh-1)

0

10

20

30

40

50

60

70

80

• Just add another column to the table you have already drawn.

*Just add the Car C data to the graph you already have.

*You will need to make the Car C line different to the Car A and Car B lines.

Time (s) Speed Skier 1 (ms-1)

Speed Skier 2 (ms-1)

0 0 0

1 5 10

2 10 20

3 15 30

4 20 40

5 25 50

Copy

•Plot a speed – time graph using this data.

•Plot the two skiers on the same axes.

•Draw a straight line of best fit for both skiers (use a ruler).

Speed (ms-1)

time (s)

•Calculate the slope of the two skiers.

•How quickly was skier 1 accelerating?

•How quickly was skier 2 accelerating?

Aim of the experiment:

To measure how the height of a ramp affects the speed of a marble covering 1m along flat ground.

Equipment:

•2x 1m rulers (one with a dip in it)

•Clamp stand

•Stopwatch

•Marble

Method:Conduct this experiment in pairs (or groups of 3 max).

1.Measure a clamp stand so that it is 10cm above the ground.

2.Place a ruler on the clamp stand. This will work as the ramp.

3.At the end of the ramp (lying flat on the ground), place the second ruler.

4.Let the marble travel down the ramp.

5.Start timing the marble when it hits the flat surface, and time how long it takes to travel the 1m.

6.Repeat the experiment with the clamp at 10cm, so that you have 3 times.

7.Repeat the experiment with the clamp at 20cm, 30cm and 40cm. Make sure you have 3 times for each height.

Processing your data:

1.Average your times for each ramp height.

2.Draw a graph using the averages.

3.From your data, calculate the average speed of the marble for each ramp height.

4.Calculate the acceleration of the marble for each ramp height.

This is calculated from speed-time graphs.

Once you have split up your graph, use the formula to find the area of each shape:

Square or rectangle = x-axis X y-axis [base X height]

Triangle = ½ X(x-axis X y-axis) [½ X base X height]

Copy

To do this, graphs need to be split into squares or rectangles or triangles.

You may have more than one shape on a graph.When this happens, work out the area of each shape separately and then add the areas together.

Handouts x2 – Finding the Area under Graphs and Distance from a speed-time graph

Km

Hours

Straight Motion

Straight motion is motion that have

Identify pleace!

Identify pleace!