Describing Motion: Position, Speed, Velocity, and Average Velocity (Lesson 1)

Position

  • What it is: Where an object is located, measured by how far it is and in what direction from a starting point.

  • Starting Point (Reference Point): A fixed object or place you use to tell where other things are. Like using your car to find a friend's car.

  • Imagine a Number Line: Think of the starting point as 0. Things in one direction are positive numbers, and things in the opposite are negative.

  • Distance vs. Direction: Distance tells you how far. Direction tells you which way (e.g., in front or behind).

  • Ways to Measure Distance: We use "car-lengths" in driving, but mostly it's meters (m).

  • Positive and Negative: A positive number means one direction (e.g., forward or east), a negative number means the opposite direction (e.g., backward or west).

    • Example: A red car is +15 m from your black car (it's 15 m in front). A white van is -21 m from your black car (it's 21 m behind).

    • Another Example: If the front of your black car is the starting point, the red car's front is 15 m away, and the white van's front is -21 m away.

    • Picture It: Draw a line with 0 at your starting point. Negative numbers are behind, positive numbers are in front.

Describing Position

  • How to do it: Always state both how far and in what direction from your chosen starting point.

  • Remember the Number Line: The starting point is 0. Distances going one way are positive, and the other way are negative.

  • Quick Way to Write It:

    • White van is -21 m from the black car.

    • Red car is +15 m from the black car.

  • Main Idea: Use the starting point to explain how far and in which direction another object sits.

Section 1: Position (p. 10) – Practice question

  • Question: If the front of the red car is your new starting point, how far away is the white van?

Speed and Velocity

  • Speed: How quickly an object moves; it's the distance it covers in a certain amount of time.

    • Rate (what it means): How much of something happens per unit of something else. Like how many hot dogs eaten per minute.

    • Example: Someone eats 60 hot dogs in 10 minutes. Their eating rate is 6010=6\frac{60}{10} = 6 hot dogs per minute.

    • Example: Watermelon costs 0.70<em>perpound</em>.</p></li><li><p><strong>SpeedUnits</strong>:Alwaysdistancedividedbytime,likekilometersperhour(km/h)ormeterspersecond(m/s).</p></li><li><p><strong>LookatThis</strong>:Thesamespeedcanbeshownindifferentways:</p></li><li><p>3min1smeans3m/s</p></li><li><p>6min2salsomeans3m/s</p></li><li><p>12min4salsomeans3m/s</p></li></ul></li><li><p><strong>Velocity</strong>:Thisisspeed<em>plus</em>thedirectionit′smoving.Ithasbothasize(thespeed)andadirection.</p><ul><li><p><strong>VelocityUnits/Examples</strong>:Acar′svelocitymightbe"km/hinaspecificdirection,"orarunner′sis"4m/stowardthefinishline,"asnail′sis"1.5cm/mintotheeast."</p></li><li><p><strong>ChangingVelocity</strong>:Velocitycanchange.Todescribemotionoveraperiod,weuse<em>averagevelocity</em>.</p></li></ul></li></ul><h4id="934da26b−e355−4f7d−93d6−19df8bbea451"data−toc−id="934da26b−e355−4f7d−93d6−19df8bbea451"collapsed="false"seolevelmigrated="true">Averagevelocity</h4><ul><li><p><strong>Whatitis</strong>:Thetotalchangeinanobject′sposition(displacement)dividedbythetimeittook.</p></li><li><p><strong>Formula</strong>:</p><ul><li><p>0.70 <em>per pound</em>.</p></li><li><p><strong>Speed Units</strong>: Always distance divided by time, like kilometers per hour (km/h) or meters per second (m/s).</p></li><li><p><strong>Look at This</strong>: The same speed can be shown in different ways:</p></li><li><p>3 m in 1 s means 3 m/s</p></li><li><p>6 m in 2 s also means 3 m/s</p></li><li><p>12 m in 4 s also means 3 m/s</p></li></ul></li><li><p><strong>Velocity</strong>: This is speed <em>plus</em> the direction it's moving. It has both a size (the speed) and a direction.</p><ul><li><p><strong>Velocity Units/Examples</strong>: A car's velocity might be "km/h in a specific direction," or a runner's is "4 m/s toward the finish line," a snail's is "1.5 cm/min to the east."</p></li><li><p><strong>Changing Velocity</strong>: Velocity can change. To describe motion over a period, we use <em>average velocity</em>.</p></li></ul></li></ul><h4 id="934da26b-e355-4f7d-93d6-19df8bbea451" data-toc-id="934da26b-e355-4f7d-93d6-19df8bbea451" collapsed="false" seolevelmigrated="true">Average velocity</h4><ul><li><p><strong>What it is</strong>: The total change in an object's position (displacement) divided by the time it took.</p></li><li><p><strong>Formula</strong>:</p><ul><li><p>\bar{v} = \frac{\text{change in position}}{\text{time taken}} = \frac{\text{final position} - \text{start position}}{\text{time taken}}</p></li></ul></li><li><p><strong>Example(Figure2B)</strong>:Ayellowcarmovesfromastartingpointof−70mtoanendingpointof20min3seconds.</p><ul><li><p><strong>ChangeinPosition</strong>:</p></li></ul></li><li><p><strong>Example (Figure 2B)</strong>: A yellow car moves from a starting point of -70 m to an ending point of 20 m in 3 seconds.</p><ul><li><p><strong>Change in Position</strong>:20 - (-70) = 90\,\text{m}(Itmoved90mtotal).</p></li><li><p><strong>Averagevelocity</strong>:(It moved 90 m total).</p></li><li><p><strong>Average velocity</strong>:\bar{v} = \frac{90\,\text{m}}{3\,\text{s}} = 30\,\text{m/s}</p></li><li><p><strong>Direction</strong>:East(becauseit′sthepositivedirectiononournumberline).</p></li></ul></li><li><p><strong>VelocityandDirection</strong>:</p><ul><li><p>Ifanobjectmovesinthepositivedirection,itsvelocityispositive(e.g.,30m/seast).</p></li><li><p>Ifanobjectmovesinthenegativedirection,itsvelocityisnegative(e.g.,25m/swest).</p></li></ul></li><li><p><strong>WithSigns</strong>:</p><ul><li><p>Redcar:velocityis</p></li><li><p><strong>Direction</strong>: East (because it's the positive direction on our number line).</p></li></ul></li><li><p><strong>Velocity and Direction</strong>:</p><ul><li><p>If an object moves in the positive direction, its velocity is positive (e.g., 30 m/s east).</p></li><li><p>If an object moves in the negative direction, its velocity is negative (e.g., 25 m/s west).</p></li></ul></li><li><p><strong>With Signs</strong>:</p><ul><li><p>Red car: velocity is25\,\text{m/s}west(negativedirection).</p></li><li><p>Yellowcar:velocityiswest (negative direction).</p></li><li><p>Yellow car: velocity is30\,\text{m/s}east(positivedirection).</p></li></ul></li><li><p><strong>Important</strong>:Tofullydescribevelocity,youneedtosay<em>both</em>thespeed<em>and</em>thedirection.</p></li></ul><h4id="cab257e8−01cb−4e24−990d−928f161a4360"data−toc−id="cab257e8−01cb−4e24−990d−928f161a4360"collapsed="false"seolevelmigrated="true">PositiveandNegativeVelocities</h4><ul><li><p>Theplus(+)orminus(−)signonvelocitysimplytellsyouthedirectionofmovementalongyourchosenpath.</p></li><li><p><strong>Example</strong>:Ifacarmovesfromastartofeast (positive direction).</p></li></ul></li><li><p><strong>Important</strong>: To fully describe velocity, you need to say <em>both</em> the speed <em>and</em> the direction.</p></li></ul><h4 id="cab257e8-01cb-4e24-990d-928f161a4360" data-toc-id="cab257e8-01cb-4e24-990d-928f161a4360" collapsed="false" seolevelmigrated="true">Positive and Negative Velocities</h4><ul><li><p>The plus (+) or minus (-) sign on velocity simply tells you the direction of movement along your chosen path.</p></li><li><p><strong>Example</strong>: If a car moves from a start of50\,\text{m}toanendofto an end of-25\,\text{m}in3seconds,then:</p><ul><li><p>Changeinposition:in 3 seconds, then:</p><ul><li><p>Change in position:-25 - 50 = -75\,\text{m}</p></li><li><p>Averagevelocity:</p></li><li><p>Average velocity:\bar{v} = \frac{-75\,\text{m}}{3\,\text{s}} = -25\,\text{m/s},whichmeans25m/stothewest.</p></li></ul></li><li><p>Thisshowsthatifyoumovetowardsthenegativesideofyournumberline,you′llgetanegativeaveragevelocity.</p></li></ul><h4id="b373c9a4−e60d−407b−86de−da7849da350f"data−toc−id="b373c9a4−e60d−407b−86de−da7849da350f"collapsed="false"seolevelmigrated="true">ReadingCheck(Conceptualquestion)</h4><ul><li><p>Howdoyoufigureoutanobject′saveragevelocity?</p><ul><li><p><strong>Answer</strong>:Usetheformula:, which means 25 m/s to the west.</p></li></ul></li><li><p>This shows that if you move towards the negative side of your number line, you'll get a negative average velocity.</p></li></ul><h4 id="b373c9a4-e60d-407b-86de-da7849da350f" data-toc-id="b373c9a4-e60d-407b-86de-da7849da350f" collapsed="false" seolevelmigrated="true">Reading Check (Conceptual question)</h4><ul><li><p>How do you figure out an object's average velocity?</p><ul><li><p><strong>Answer</strong>: Use the formula:\bar{v} = \frac{\text{final position} - \text{start position}}{\text{time taken}}</p></li></ul></li></ul><h4id="8ec8b970−a7ea−49a5−95af−1c6ba48b2dc9"data−toc−id="8ec8b970−a7ea−49a5−95af−1c6ba48b2dc9"collapsed="false"seolevelmigrated="true">Connections,implications,andreal−worldrelevance</h4><ul><li><p><strong>PerspectiveMatters</strong>:Position,speed,andvelocityalwaysdependonyourchosenstartingpointordirection.</p></li><li><p><strong>EverydayUse</strong>:Knowingtheseconceptshelpswithdrivingsafely,navigating,andunderstandinghowthingsmovearounduseveryday.</p></li><li><p><strong>SafetyFirst</strong>:Accuratemeasurementsofwherethingsareandhowfastthey′regoingarecrucialfordrivingsafetyandunderstandingmotion.</p></li></ul><h4id="812b7044−a4df−4131−9ddc−3ff2fe1aad42"data−toc−id="812b7044−a4df−4131−9ddc−3ff2fe1aad42"collapsed="false"seolevelmigrated="true">Quickformulastoremember</h4><ul><li><p><strong>ChangeinPosition(Displacement)</strong>:</p></li></ul></li></ul><h4 id="8ec8b970-a7ea-49a5-95af-1c6ba48b2dc9" data-toc-id="8ec8b970-a7ea-49a5-95af-1c6ba48b2dc9" collapsed="false" seolevelmigrated="true">Connections, implications, and real-world relevance</h4><ul><li><p><strong>Perspective Matters</strong>: Position, speed, and velocity always depend on your chosen starting point or direction.</p></li><li><p><strong>Everyday Use</strong>: Knowing these concepts helps with driving safely, navigating, and understanding how things move around us every day.</p></li><li><p><strong>Safety First</strong>: Accurate measurements of where things are and how fast they're going are crucial for driving safety and understanding motion.</p></li></ul><h4 id="812b7044-a4df-4131-9ddc-3ff2fe1aad42" data-toc-id="812b7044-a4df-4131-9ddc-3ff2fe1aad42" collapsed="false" seolevelmigrated="true">Quick formulas to remember</h4><ul><li><p><strong>Change in Position (Displacement)</strong>:\Delta x = \text{final position} - \text{start position}</p></li><li><p><strong>TimeTaken</strong>:</p></li><li><p><strong>Time Taken</strong>:\Delta t(orjust(or justtifyoustartcountingfromzero)</p></li><li><p><strong>AverageVelocity</strong>:if you start counting from zero)</p></li><li><p><strong>Average Velocity</strong>:\bar{v} = \frac{\text{change in position}}{\text{time taken}} = \frac{\text{final position} - \text{start position}}{\text{time taken}}</p></li><li><p><strong>Speed</strong>:</p></li><li><p><strong>Speed</strong>:\text{speed} = \frac{\text{distance}}{\text{time}}</p></li><li><p><strong>Velocity(withdirection)</strong>:Speedplusaspecificdirection(e.g.,</p></li><li><p><strong>Velocity (with direction)</strong>: Speed plus a specific direction (e.g.,\bar{v} = 30\,\text{m/s east}$$)