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Displacement and Velocity Chapter 2 Section 1

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Displacement Definitions Displacement – The change in position of an object from one point to another in a straight line with direction. Distance – A scalar quantity that is the length of travel, neglecting direction. Position – The location of an object relative to the origin.

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Definitions Continued… Instantaneous Position – The location of an object at a particular instant in time relative to the origin. Origin – The zero point or where an object begins its motion. Magnitude – A term given to the size of a quantity.

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SI Units for Displacement and Distance The SI units for distance and displacement are: – Meters m

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Displacement vs. Distance Displacement is not equal to the distance traveled. – Displacement: A vector quantity – Distance : A scalar quantity

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Coordinate system The coordinate system is used to show motion in a certain direction. – x-y coordinate system

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Displacement Equation Δx = x f – x i Δx = displacement or change in position x f = final position X i = initial position

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Explanation of the Variables “Δ” Is the Greek letter Delta and it means, “Change in.” The values of “x f ” and “x i “ and are determined by their positions to the origin. When solving for the displacement, make sure the units are the same for the initial and final positions. – Example: All the units should be in meters.

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Displacement Direction Displacement can be in any direction, but horizontal movement is denoted with “Δx” and vertical movement is denoted with “Δy” – Just like the coordinate plane Y is vertical X is horizontal

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Displacement Signs Displacement can either be positive or negative. The negative sign represents the direction of the magnitude. – If x f is less than x i, then Δx will be negative. Displacement is an example of a quantity that has both magnitude and direction.

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Coordinates and Signs In one-dimensional motion, there are only two directions in which an object can move, which is specified by “positive” or “negative.” You could also look at it as forward and backwards. – Anything to the right of the origin will be considered positive and anything to the left will be considered negative. – In two dimensions, anything above the origin is considered positive and below is negative.

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Example Problem A car left a stop light and traveled forward to a store located 80 meters away. If a gym is located 15 meters away from the stop light, what is the displacement from the gym to the store?

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Example Problem Answer Δx = x f – x i Δx = 80m – 15m Δx = 65 meters The total displacement was 65 meters. Light @ 0 m Gym @ 15 m Store @ 80 m

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Velocity Definitions Velocity – A vector quantity that measures how fast something moves from one point to another with direction. Speed – A scalar quantity that measures how fast something moves, neglecting direction. – Ex: Speedometer in your car shows speed, not velocity

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Velocity Definitions Cont… Average Velocity – Is equal to the displacement divided by the time during which the displacement occurred. Instantaneous Velocity – The speed and direction of an object at a single instant moment in time. Time Interval – Represents the change in time.

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SI Units of Velocity The SI units for velocity are: – Meters per second – Meters/Second m/s

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Average Velocity Equation Δx = Change in Position (Displacement) Δt = Change in Time (Time interval)

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Velocity vs. Speed Velocity is not the same as speed. – Velocity has both magnitude and direction (vector) – Speed has only magnitude (scalar)

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Example Problem During a drag car race, the car covers a quarter mile in 12 seconds, while going down the track due east. What is the average velocity of the car in miles per hour?

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Example Problem Answers

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Graphing Velocity

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Displacement vs. Time Graph time Displacement Slope = velocity

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Analysis of a V vs. t graph

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Velocity vs. Time Graph time Area under slope = Displacement Velocity

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