Displacement and Velocity Chapter 2 Section 1

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.

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.

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

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

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

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

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.

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

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.

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.

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?

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

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

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.

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

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

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

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?

Example Problem Answers

Graphing Velocity

Displacement vs. Time Graph time Displacement Slope = velocity

Analysis of a V vs. t graph

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