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 positionxf = final positionXi = 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

Δx = xf – xi

Δx = 80m – 15mΔx = 65 meters

The total displacement was 65 meters.

Light @ 0 mGym @ 15 m

Store @ 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)

𝑣𝑎𝑣𝑔=∆ 𝑥∆ 𝑡 =

𝑥 𝑓 −𝑥 𝑖

𝑡 𝑓 −𝑡 𝑖

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

𝑉 𝑎𝑣𝑔=∆ 𝑥∆𝑡 =

0.25𝑚𝑖𝑙𝑒12𝑠𝑒𝑐 𝑥 3600 𝑠𝑒𝑐

1h𝑟 =75 h𝑚𝑝 𝑑𝑢𝑒𝐸𝑎𝑠𝑡

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 vs. Time Graph

time

DisplacementSlope = velocity

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

time

Area under slope = Displacement

Velocity