How can you tell the image in each frame is
moving?
Look at the runners position relative to the
background. The position changes relative to
stationary objects in the background.
1
STILL
1
2
3
4
ACCELERATING – INCREASING SPEED
2
3
4
5
CONSTANT SPEED
5
1
2
3
4
5
ACCELERATING – DECREASING SPEED
A series of images of a moving object that records its
position after equal time intervals is called a motion
diagram.
Replacing an object by a single point is called the
particle model.
But to use the particle model, you must make sure that
the size of the object is much less than the distance it
moves,
Where and When?
We use a co-ordinate system to show where
the motion begins (zero) and which direction
the variables increase.
POSITIVE DIRECTION
You can locate the position of a sprinter at a particular time
on a motion diagram by drawing an arrow from the origin to
the belt of the sprinter.
The arrow is called a POSITION VECTOR– PROPORTIONAL
TO THE DISTANCE FROM THE ORIGIN
A negative Position Vector
Vectors and Scalars
• A quantity such as these that tells you only the
magnitude of something is called a scalar quantity.
• A vector quantity tells you not only the
magnitude of the quantity, but also its direction.
Vectors and Scalars
• A quantity such as these that tells you only the
magnitude of something is called a scalar quantity.
Only Magnitude
• Example: Longview is 20 miles from Sabine HS This is a
scalar quantity because it only tells the magnitude of the
distance.
Vectors and Scalars
• A vector quantity tells you not only the
magnitude of the quantity, but also its direction.
Magnitude
Direction
• Longview is 20 miles to the northeast of Sabine HS. This
is a vector quantity because it tells the magnitude and
the direction.
A vector quantity tells you not
only the magnitude of the
quantity, but also its direction.
A quantity such as these
that tells you only the
magnitude of something
is called a scalar
quantity.
Time Intervals and Displacements
The motion of the runner depends upon both the scalar
quantity time and the vector quantity displacement.
Displacement defines the distance and direction
between two positions.
How long did it take to go from 0 to 50 meters?
How long did it take to go from 0 to 50 meters?
The difference between t0 and t1 is the time interval.
A common symbol for the time interval is Δt.
Δt = t1 - t0
d0
d1
What was the change in position of the sprinter as she
moved from the starting block to midway in the race?
CHANGE IN
POSITION
d0
d1
An arrow is drawn from the runner’s initial position, d0, to
her position 50 m along the track, d1.
This arrow is called a displacement vector and is represented
by the symbol d.
d0
d1
The change in position of an object is called its
displacement.
d0
d1
The length, or size, of the displacement vector is called
the distance between the two positions.
That is, the distance the runner moved fromd0 to d1 was
50 m.
Distance is a scalar quantity.
The displacement of an object that moves from position
d0 to d1 is given by
Δd = d1 – d0.
d is the symbol we use to represent position
Δd is the distance traveled
Velocity
Average Velocity is the change in
position / the amount of time it
took to get there
Velocity
If it took you .5 hour to go 20 miles to
Longview, your average velocity = 20miles/.5
hour = 40 m/h
Velocity is a vector. Velocity has magnitude
and direction.
If direction changes, the velocity changes.
• Velocity is magnitude and direction of motion.
•
If either the magnitude or direction changes, then the
velocity changes.
•
If you are going around a curve or in a circle, your
direction is changing and thus your velocity is changing.
The average speed is the ratio of the total distance
traveled to the time interval.
Automobile speeds are measured in miles per hour
(mph) or kilometers per hour (km/h), but in this course,
the usual unit will meters per second (m/s).
V = d1-d0 / time
d1-d0 is change of position or distance
traveled
Instantaneous velocity
Why average velocity?
A motion diagram tells you the position
of a moving object at the beginning and
end of a time interval. It doesn’t tell you
what happened within the time interval.
What if you want to know the speed and direction of
an object at a particular instant in time? The quantity
you are looking for is instantaneous velocity.
This is like you look at the speedometer and see you
are going 55 m/h at this particular instant.
In this course, the term velocity will refer to
instantaneous velocity, represented by the symbol v.
Average velocity motion diagrams How
can you show average velocity on a motion
diagram?
Although the average velocity vector is in
the same direction as displacement, the two
vectors are not measured in the same units.
Nevertheless, they are proportional; when
displacement is larger over a given time
interval, so is average velocity
Average velocity vectors have the same direction
as their corresponding displacement vectors. Their
magnitudes are different but proportional, and they
have different units.
Create pictorial and physical models for each of the following problems. Do not solve the
problem.
A hockey puck’s average velocity is 22 m/s. What is its displacement in 6.0 s?
Create pictorial and physical models for each of the following problems. Do not solve the
problem.
A hockey puck’s average velocity is 22 m/s. What is its displacement in 6.0 s?
The definition of average velocity, v = d/t,
Rearrange the equation v = d/t by multiplying
both sides by t and you get…
Displacement from Average Velocity and Time…
What direction is positive velocity? That depends on how
you define the co-ordinate system . The direction of the
velocity vector will be in the same direction as the
displacement vector, but…
+X
+X
Acceleration
The average velocity of the golf ball was
changing from one time interval to the next. You
can tell because the average velocity vectors in
each time interval have different magnitudes
An object in motion whose velocity is
changing is said to be accelerating.
Velocity is magnitude and direction of motion. If either the
magnitude or direction changes, then the velocity changes.
If you are going around a curve or in a circle, your direction
is changing and thus your velocity is changing.
Acceleration is the change in velocity during some
period of time. Velocity is meters / second
Acceleration is increase or decrease in velocity over
some period of time –
Δv / Δt
------- Vf – Vi / Tf – Ti
Vf – Vi m/s
/
Tf – Ti s
Meters / second / second ---- m/s2
Example: a = 2m/s2
Every second, the velocity increases by 2m/s
1s v = 2m/s
2s v = 4 m/s
3s v = 6 m/s
Example: a = 10m/s2
Every second, the velocity increases by 10m/s
1s v = 10m/s
2s v = 20 m/s
3s v = 30 m/s
An object in motion whose velocity is
changing is said to be accelerating.
Velocity is magnitude and direction of motion. If either the
magnitude or direction changes, then the velocity changes. If
you are going around a curve or in a circle, your direction is
changing and thus your velocity is changing.
Therefore if your direction is changing,
you are accelerating.
Watch this video closely. How many changes in direction and
magnitude of velocity can you count.
Using motion diagrams to obtain average
acceleration
How can you find the change in average velocity using
motion diagrams?
Motion diagrams indicate position and time. From position
and time, you can determine average velocity. You can get a
rough idea, or qualitative description, of acceleration by
looking at how the average velocity changes.
In a motion diagram, the average acceleration vector, a
is proportional to the change in the average velocity
vector, v.
You can draw the average acceleration and change in
average velocity vectors the same length, but different
colors.
In this diagram, the origin is on the left. As a result, all
the average velocity vectors are positive. The sign of
the acceleration is determined by whether the car is
speeding up or slowing down.
The direction of the acceleration is determined by
whether the car is speeding up, slowing down, or
traveling at constant speed.
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