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It emphasizes direction-changing acceleration at turning points and introduces how velocity, position, and acceleration graphs connect through slopes and areas.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/lecture-3-day-2-motion-and-kinematics-acceleration-complete-motion-diagrams-and-turning-points/656998/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/lecture-3-day-2-motion-and-kinematics-acceleration-complete-motion-diagrams-and-turning-points/656998.png","ImageObject",300,407,{"name":42,"@type":43},"River Wang","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How does acceleration relate to changing velocity?","Question",{"text":63,"@type":64},"Acceleration is what changes an initial velocity into a final velocity. When acceleration is opposite the velocity, the object slows down; when aligned with velocity, it speeds up.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why can acceleration exist even when speed is constant on a curve?",{"text":68,"@type":64},"Because the velocity direction changes. Even if the magnitude stays constant, the change in velocity direction means acceleration is nonzero and points toward the center of the circular path.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the acceleration at a turning point?",{"text":72,"@type":64},"At the turning point, acceleration cannot be zero by the definition of acceleration as the change from an initial velocity to a final velocity. 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But what changes an initial velocity to a final velocity? Acceleration is what changes an initial velocity to a final velocity.  \nThe definition of velocity is:  \na = \"\"vt \\# \"v = a\" t v f = vi + a\" t or vf = vi + \"v  \nSince we know how to add and subtract vectors , let’s do an example of a motion diagram and find acceleration.  \nExample:  \nA spacecraft lands on Mars with a parachute. Draw a motion diagram to describe the motion.  \nvi  \nΔv  \nΔv  \n Δv  \nvf  \nΔv  \nSo we can see that the spacecraft is slowing down and that our acceleration vectors are pointing in the direction opposite to the velocity.  \nLet’s do a few simple examples of a car on a track:  \nDraw the velocity and acceleration vectors for the car speeding up:  \na a a  \nNotice for the car speeding up the acceleration points in the same direction as the velocity.  \nNow try the car going around a curve at constant velocity:  \nNotice that going around a curve at constant velocity there is an acceleration. But by definition , a = \"tv , if vi = vf , Δv = 0 so a = 0. This would imply that going around a curve at constant velocity , acceleration should be zero! So why is a≠0? Think about this while trying your own diagram: a car going over the opposite curve at constant velocity.  \nSo let’s answer the question , how can you have an acceleration at constant velocity? The truth is , the magnitude is constant , but the direction is changing. So there has to be an acceleration if the velocity is changing direction , because acceleration is what changes an initial velocity to a final velocity. Also notice that the acceleration points to a common point , the center of the circle. It makes sense if you think about it , to keep something going in a circle you have to have an acceleration toward the center. Think of a ball on a string , which you swing around. If you cut the string the ball will go off in a new direction – no longer in a circle. The string is what provides that acceleration to keep it in a circle.  \nNow we’ll have you do some examples:  \n• A car rolls down a hill after the parking brake fails  \n• Bob runs once around a track with straight sides and semicircular ends  \n• A ferris wheel goes around once at constant speed  \na  \na = 0  \na = 0  \nNo acceleration on the straight bits , but notice that acceleration points to the center of the semi-circles.  \nAcceleration for the ferris wheel should point toward the center.  \nEven though the speed of the ferris wheel doesn’t change , there is an acceleration because the direction of the velocity is changing. So now let’s try a quick quiz question.  \nA car drives over a hill at a steady 60 mph. Is it accelerating as it crosses the crest of a hill? Justify your answer using a complete motion diagram  \nNow let’s consider a new type of situation:  \n[cart attached to mass over pulley , push against force of mass and allow to return]  \nNow let’s do a motion diagram including velocity and acceleration vectors.  \na a a  \na a a  \nNotice something very important , the object slows down when acceleration is opposite velocity , and the object speeds up when acceleration is in the same direction as velocity.  \nWhat about the turning point , what’s the acceleration there?  \nWe’ll split the class into two groups , since there are two possibilities: a = 0 , a≠0 each has to choose a spokesman and defend the position.  \nUltimately , acceleration at the turning point cannot be zero by the definition of acceleration – acceleration is what changes initial velocity to final velocity.  \nIf we look at the vectors:  -vi  vf   \nΔv  \nΔv is definitely not equal to zero. In fact it is pretty big compared to the other acceleration vectors. This is because you have to go from velocity to the left to a change that gives you velocity","cbCaitqcxg3vr9ok","https://ap.wps.com/l/cbCaitqcxg3vr9ok","pdf",187153,"English","# Acceleration\n## Velocity-to-velocity change (motion diagrams)\n## Direction vs magnitude in constant-speed motion\n## Turning points and nonzero acceleration\n## Practice examples and quiz\n## Cart-pulley motion diagram with vectors\n## Position, velocity, and acceleration graphs","[{\"question\":\"How does acceleration relate to changing velocity?\",\"answer\":\"Acceleration is what changes an initial velocity into a final velocity. When acceleration is opposite the velocity, the object slows down; when aligned with velocity, it speeds up.\"},{\"question\":\"Why can acceleration exist even when speed is constant on a curve?\",\"answer\":\"Because the velocity direction changes. Even if the magnitude stays constant, the change in velocity direction means acceleration is nonzero and points toward the center of the circular path.\"},{\"question\":\"What is the acceleration at a turning point?\",\"answer\":\"At the turning point, acceleration cannot be zero by the definition of acceleration as the change from an initial velocity to a final velocity. The motion diagram vectors show a significant change in velocity direction.\"}]","Lecture 3 - Day 2 Motion and Kinematics - Acceleration - Complete Motion Diagrams and Turning Points | PDF",1792972401,18]