chapter 2 kinematics: description of motion. units of chapter 2 distance and speed: scalar...
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Chapter 2Kinematics: Description of
Motion
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Units of Chapter 2
Distance and Speed: Scalar Quantities
One-Dimensional Displacement and Velocity: Vector Quantities
Acceleration
Kinematic Equations (Constant Acceleration)
Free Fall
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2.1 Distance and Speed: Scalar Quantities
Distance is the path length traveled from one location to another. It will vary depending on the path.
Distance is a scalar quantity—it is described only by a magnitude.
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2.1 Distance and Speed: Scalar Quantities
Average speed is the distance traveled divided by the elapsed time:
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2.1 Distance and Speed: Scalar Quantities
Since distance is a scalar, speed is also a scalar (as is time).
Instantaneous speed is the speed measured over a very short time span. This is what a speedometer reads.
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
A vector has both magnitude and direction. Manipulating vectors means defining a coordinate system, as shown in the diagrams to the left.
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Displacement is a vector that points from the initial position to the final position of an object.
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Note that an object’s position coordinate may be negative, while its velocity may be positive; the two are independent.
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
For motion in a straight line with no reversals, the average speed and the average velocity are the same.
Otherwise, they are not; indeed, the average velocity of a round trip is zero, as the total displacement is zero!
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Different ways of visualizing uniform velocity:
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2.2 One-Dimensional Displacement and Velocity: Vector Quantities
This object’s velocity is not uniform. Does it ever change direction, or is it just slowing down and speeding up?
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2.3 Acceleration
Acceleration is the rate at which velocity changes.
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2.3 AccelerationAcceleration means that the speed of an object is changing, or its direction is, or both.
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2.3 Acceleration
Acceleration may result in an object either speeding up or slowing down (or simply changing its direction).
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2.3 AccelerationIf the acceleration is constant, we can find the velocity as a function of time:
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2.4 Kinematic Equations (Constant Acceleration)
From previous sections:
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2.4 Kinematic Equations (Constant Acceleration)
Substitution gives:
and:
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2.4 Kinematic Equations (Constant Acceleration)
These are all the equations we have derived for constant acceleration. The correct equation for a problem should be selected considering the information given and the desired result.
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2.5 Free Fall
An object in free fall has a constant acceleration (in the absence of air resistance) due to the Earth’s gravity.
This acceleration is directed downward.
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2.5 Free Fall
The effects of air resistance are particularly obvious when dropping a small, heavy object such as a rock, as well as a larger light one such as a feather or a piece of paper.
However, if the same objects are dropped in a vacuum, they fall with the same acceleration.
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2.5 Free Fall
Here are the constant-acceleration equations for free fall:
The positive y-direction has been chosen to be upwards. If it is chosen to be downwards, the sign of g would need to be changed.
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Summary of Chapter 2
Motion involves a change in position; it may be expressed as the distance (scalar) or displacement (vector).
A scalar has magnitude only; a vector has magnitude and direction.
Average speed (scalar) is distance traveled divided by elapsed time.
Average velocity (vector) is displacement divided by total time.
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Summary of Chapter 2
Instantaneous velocity is evaluated at a particular instant.
Acceleration (vector) is the time rate of change of velocity.
Kinematic equations for constant acceleration:
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Summary of Chapter 2
An object in free fall has a = –g.
Kinematic equations for an object in free fall: