Displacement and Velocity

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 = xf – xi Δx = displacement or change in position xf = final position Xi = initial position

Explanation of the Variables • “Δ” Is the Greek letter Delta and it means, “Change in.” • The values of “xf”and “xi“ 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 xf is less than xi, 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 Light @ 0 m Store @ 80 m Gym @ 15 m Δx = xf – xi Δx = 80m – 15m Δx = 65 meters The total displacement was 65 meters.

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 • Velocity can be interpreted graphically by the slope on a displacement vs. time graph. Slope of a line for a d vs. t graph

Displacement Slope = velocity time Displacement vs. Time Graph

Analysis of a V vs. t graph • The area under the slope on a Velocity vs. Time graph is equal to the displacement. • The length would be the velocity and the width would be the time.

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

Displacement and Velocity