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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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Position Separation between object and a reference point.

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Instantaneous Position Position of object at a specific time

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Scalar Quantity that has only a magnitude or size. It is just a measurement.

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Magnitude Size 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 Acceleration The 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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Formulas

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Position-time Graph Graph 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 -

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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.

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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

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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

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(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.

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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

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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

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(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.

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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.

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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)

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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.

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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 downward sloping line since the object has - acceleration (again, the slope = acceleration for v-t graphs)

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