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**Chapter 2 Kinematics: 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 Acceleration Acceleration 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 Acceleration If 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:

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