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1 Chapter 3 Kinematics-The Study Of Motion

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2 Introduction Kinematics: The branch of mechanics that studies the motion of an object without regard to the cause of the motion. To describe motion we must define the position of a body. Displacement is a change in the position of an object, a vector quantity.

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3 The average velocity of an object is its displacement divided by the time it takes for that displacement. Introduction

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4 The units for velocity can vary, but are always a unit of displacement over a unit of time. Common SI units include meters per second (m/s) and kilometers per hour (km/h). Common British units include feet per second (ft/s) and miles per hour (mi/h or mph). Introduction

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5 Average velocity is a vector quantity based upon the displacement of an object. The average speed of an object is the distance an object moves per unit of time. Speed is a scalar quantity because distance is a scalar quantity. Introduction

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6 Constant Velocity Whenever an object moves in such a way that it always travels equal distances in equal times, the object is said to be moving at constant velocity. Analysis of a displacement-time graph of constant velocity will reveal points of equal spacing along a straight line, the slope of which is the velocity.

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7 Constant Acceleration The change in velocity of an object over a period of time is acceleration. Change in velocity could be a change in speed or direction. The common units for acceleration are m/s/s (m/s 2 ) or ft/s/s (ft/s 2 ).

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8 Instantaneous Velocity The instantaneous velocity of an object is its velocity at an exact moment of time. The speedometer on a car indicates instantaneous velocity.

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9 Kinematics in One Dimension Calculating final velocity when initial velocity, acceleration and time are known. Calculating average velocity from initial and final velocities.

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10 Kinematics in One Dimension Calculating displacement when given initial velocity, final velocity and time. (Constant Acceleration) Calculating displacement from initial velocity,acceleration and time.

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11 Kinematics in One Dimension Calculating final velocity when given initial velocity, acceleration and displacement. The equation that you use to solve the problem depends entirely upon what is given in the problem and what you are solving for. Neatly organizing your work is the key to success.

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12 Freely Falling Body A freely falling body is one that moves freely under the influence of gravity. Gravity (g) is an acceleration towards the center of earth (or any other body). The rate of gravity on earth is -9.80 m/s 2 or -32.2 ft/s 2 for all objects. g can be substituted into any existing acceleration equation.

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13 Freely Falling Body

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14 Projectile Motion In Two Dimensions Motion in both the vertical and horizontal planes is projectile motion in two dimensions. The vertical motion is completely independent from the horizontal motion. The path that the object takes through space is called its trajectory.

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15 Projectile Motion In Two Dimensions: Objects Fired Horizontally Step 2: Calculate the range (x). Step 1: Calculate the drop time.

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16 Projectile Motion In Two Dimensions: Objects Fired At An Angle Step 2: Calculate the range (x). Step 1: Resolve projectile velocity into its x and y components.

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