linear kinematics. kinematics study of motion of objects without regard to the causes of this motion
TRANSCRIPT
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Linear Kinematics
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Kinematics
Study of motion of objects without regard to the causes of
this motion.
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Linear
Relationship between variables acted in the same
plane.
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Reference Point
Zero location in a coordinate system or reference frame
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PositionSeparation between object
and a reference point.
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Instantaneous PositionPosition of object at a
specific time
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ScalarQuantity that has only a
magnitude or size. It is just a measurement.
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MagnitudeSize or measurement
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Vector
Quantity having both magnitude and direction.
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Distance
The separation between
two points. A scalar quantity.
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Displacement
Change in position. A
vector quantity.
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Speed
Ratio of distance to time
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Velocity
Ratio of change in position to time interval over which
change takes place.
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Instantaneous Velocity
The velocity of an object at a specific point in time.
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Initial Velocity
Velocity of object at
time: t=0 s or when
recording starts.
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Final Velocity
The velocity of the object at the point of time in question or
when recording stops.
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Acceleration
Change in velocity divided by time interval over which it
occurred.
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Instantaneous AccelerationThe measurement of the acceleration of an object at a specific point in
time.
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Gravity
The acceleration an object has towards the mass it is
attracted.
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FormulasV
d
tdf ditf t i
a V
tVf Vitf t i
Vf Vi at
d Vit 12 at
2V2 f V2 i 2ad
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Position-time GraphGraph of object’s motion that
shows how its position depends on time.
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Velocity-time Graph
Plot of velocity of object as a function of time.
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moving with a constant, positive velocity is shown. A positive, constant velocity is represented by a line with
constant slope (straight) and positive slope (upwards
sloping).
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moving with a constant, negative velocity is shown. A negative, constant velocity is
represented by a line with constant slope (straight)
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moving in the + dir'n and accelerating from a low
velocity to a high velocity is shown. If the object is moving in the + dir'n, then the slope of a p-t graph would be +.
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If the object is changing velocity from small to large values, then the slope must change from small slope to
large slope.
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moving in the + dir'n and accelerating from a high
velocity to a low velocity is shown. If the object is moving in the + dir'n, then the slope of a p-t graph would be +.
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If the object is changing velocity from high to low
values, then the slope must change from high slope to
low slope.
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moving in the - dir'n and accelerating from a high
velocity to a low velocity is shown. If the object is moving in the - dir'n, then the slope of
a p-t graph would be -.
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If the object is changing velocity from high to low
values, then the slope must change from high slope to
low slope.
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moving in the - dir'n and accelerating from a low
velocity to a high velocity is shown. If the object is moving in the - dir'n, then the slope of
a p-t graph would be -.
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If the object is changing velocity from low to high
values, then the slope must change from low slope to
high slope.
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moving in the + dir'n with constant speed; first a slow constant speed and then a
fast constant speed is shown. If an object is moving in the +
dir'n, then the slope of the line on a p-t graph would be
+.
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At first, the line has a small slope (corresponding to a
small velocity) and then the line has a large slope
(corresponding to a large velocity).
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moving in the + dir'n with constant speed; first a fast constant speed and then a
slow constant speed is shown. If an object is moving in the + dir'n, then the slope
of the line on a p-t graph would be +.
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At first, the line has a large slope (corresponding to a
large velocity) and then the line has a small slope
(corresponding to a small velocity).
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moving in the - dir'n with constant speed; first a slow constant speed and then a
fast constant speed is shown. If an object is moving in the -
dir'n, then the slope of the line on a p-t graph would be
-.
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At first, the line has a small slope (corresponding to a
small velocity) and then the line has a large slope
(corresponding to a large velocity).
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moving in the - dir'n with constant speed; first a fast constant speed and then a
slow constant speed is shown. If an object is moving in the - dir'n, then the slope of the line on a p-t graph would
be -.
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At first, the line has a large slope (corresponding to a
large velocity) and then the line has a small slope
(corresponding to a small velocity).
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moves in the + direction at a slow constant speed and
then in a - direction at a fast constant speed is shown.
The object must first have a + slope
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(corresponding to its + velocity) then it must have a - slope (corresponding to its -
velocity). Initially, the slope is small (corresponding to a
small velocity) and then the slope is large (corresponding
to a large velocity).
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moves in the + direction at a fast constant speed and then
in a - direction at a slow constant speed is shown. The
object must first have a + slope (corresponding to its +
velocity) then it must have a - slope
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(corresponding to its - velocity). Initially, the slope is
large (corresponding to a large velocity) and then the
slope is small (corresponding to a small velocity).
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moves in the - direction at a slow constant speed and then
in a + direction at a fast constant speed is shown. The object must first have a - slope (corresponding to its - velocity)
then it must have a + slope
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(corresponding to its + velocity). Initially, the slope is
small (corresponding to a small velocity) and then the
slope is large (corresponding to a large velocity).
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A velocity-time graph for an object moving with a constant speed in the positive direction
is shown. To have "a constant speed in the positive
direction" is to have a + velocity which is unchanging.
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Thus, the line on the graph will be in the + region of the graph (above 0). Since the velocity is unchanging, the line is horizontal. Since the
slope of a line on a v-t graph
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is the object's acceleration, a horizontal line (zero slope) on a v-t graph is characteristic of
a motion with zeo acceleration (constant
velocity).
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moving with a constant speed in the negative direction is
shown. To have "a constant speed in the negative
direction" is to have a - velocity which is unchanging.
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Thus, the line on the graph will be in the - region of the graph (below 0). Since the velocity is unchanging, the line is horizontal. Since the
slope of a line on a v-t graph
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is the object's acceleration, a horizontal line (zero slope) on a v-t graph is characteristic of
a motion with zeo acceleration (constant
velocity).
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an object which is at rest is shown. To be "at rest" is to have a zero velocity. Thus the line is drawn along the
axis (v=0).
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moving in the + direction, accelerating from a slow speed to a fast speed is shown below. An object which is moving in the +
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direction and speeding up (slow to fast) has a +
acceleration. (If necessary, review the dir'n of the
acceleration vector in the Physics Classroom.) Since
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the slope of a line on a v-t graph is the object's
acceleration, an object with + acceleration is represented by a line with + slope. Thus, the line is a straight diagonal line with upward (+) slope.
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Since the velocity is +, the line is plotted in the + region
of the v-t graph.
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moving in the + direction, accelerating from a fast
speed to a slow speed is shown. An object which is
moving in the + direction and slowing down
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(fast to slow) has a - acceleration. (If necessary,
review the dir'n of the acceleration vector in the
Physics Classroom.) Since the slope of a line on a v-t
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graph is the object's acceleration, an object with -
acceleration is represented by a line with - slope. Thus, the line is a straight diagonal line
with downward (-) slope. Since the velocity is +, the line is
plotted in the + region of the v-t graph.
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moving in the - direction, accelerating from a slow speed to a fast speed is
shown. An object which is moving in the - direction and
speeding up (slow to fast) has a -
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acceleration. (If necessary, review the dir'n of the
acceleration vector in the Physics Classroom.) Since the slope of a line on a v-t
graph is the object's acceleration, an object with -
![Page 82: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/82.jpg)
acceleration is represented by a line with - slope. Thus,
the line is a straight diagonal line with downward (-) slope. Since the velocity is -, the line is plotted in the - region of the
v-t graph.
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moving in the - direction, accelerating from a fast
speed to a slow speed is shown. An object whgich is moving in the - direction and slowing down (fast to slow)
has a +
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acceleration. (If necessary, review the dir'n of the
acceleration vector in the Physics Classroom.) Since the slope of a line on a v-t
graph is the object's acceleration, an object with + acceleration is represented
by a line with + slope.
![Page 86: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/86.jpg)
Thus, the line is a straight diagonal line with upward (+) slope. Since the velocity is -,
the line is plotted in the - region of the v-t graph.
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first moves with a slow, constant speed in the +
direction, and then with a fast constant speed in the +
direction is shown below. Since there are two parts of
this object's motion, there will be two distinct parts on the
![Page 89: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/89.jpg)
graph. Each part is in the + region of the v-t graph (above
0) since the velocity is +. Each part is horizontal since the velocity during each part
is constant
![Page 90: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/90.jpg)
(constant velocity means zero acceleration which means zero slope). The
second part of the graph will be higher since the velocity is
greater during the second part of the motion.
![Page 91: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/91.jpg)
![Page 92: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/92.jpg)
first moves with a fast, constant speed in the +
direction, and then with a slow constant speed in the +
direction is shown. Since there are two parts of this object's motion, there will
![Page 93: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/93.jpg)
be two distinct parts on the graph. Each part is in the +
region of the v-t graph (above 0) since the velocity is +.
Each part is horizontal since the velocity during each part
is constant
![Page 94: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/94.jpg)
(constant velocity means zero acceleration which
means zero slope). The first part of the graph will be higher since the velocity is
greater during the first part of the motion.
![Page 95: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/95.jpg)
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first moves with a constant speed in the + direction, and then moves with a positive
acceleration is shown. Since there are two parts of this
object's motion, there will be two distinct parts on the
graph.
![Page 97: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/97.jpg)
Each part is in the + region of the v-t graph (above 0) since the velocity is +. The slope of
the first part is zero since constant velocity means zero
acceleration and zero acceleration is represented
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by a horizontal line on a v-t graph (slope = acceleration for v-t graphs). The second
part of the graph is an upward sloping line since the
object has + acceleration (again, the slope =
acceleration for v-t graphs)
![Page 99: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/99.jpg)
![Page 100: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/100.jpg)
first moves with a constant speed in the + direction, and then moves with a negative acceleration is shown. Since
there are two parts of this object's motion, there will be
two distinct parts on the graph.
![Page 101: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/101.jpg)
Each part is in the + region of the v-t graph (above 0) since the velocity is +. The slope of
the first part is zero since constant velocity means zero
acceleration and zero acceleration is represented
![Page 102: Linear Kinematics. Kinematics Study of motion of objects without regard to the causes of this motion](https://reader036.vdocuments.net/reader036/viewer/2022062314/56649e0c5503460f94af5a1f/html5/thumbnails/102.jpg)
by a horizontal line on a v-t graph (slope = acceleration for v-t graphs). The second
part of the graph is an downward sloping line since the object has - acceleration
(again, the slope = acceleration for v-t graphs)