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For multiple given polynomials and specified time intervals, the tasks include computing displacement and distance traveled, velocity v(t), and acceleration a(t). Students also determine maximum speed with its occurrence times, identify direction changes, classify motion as left/right, and locate when acceleration is zero as well as when the particle speeds up or slows down, using blank graphs for sketches.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/motion-along-a-line-problem-set-velocity-acceleration-and-displacement/522865/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/motion-along-a-line-problem-set-velocity-acceleration-and-displacement/522865.png","ImageObject",300,407,{"name":92,"@type":93},"Angel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How are velocity v(t) and acceleration a(t) obtained from the position function s(t)?","Question",{"text":113,"@type":114},"Velocity is found by differentiating s(t) with respect to t, and acceleration is found by differentiating v(t) (equivalently, differentiating s(t) twice).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does the worksheet ask for besides v(t) and a(t) in the direction-change problems?",{"text":118,"@type":114},"It requires the times when the particle changes directions, the intervals when it moves left versus right, the times when acceleration equals 0, and the intervals when the particle is slowing down or speeding up.",{"name":120,"@type":111,"acceptedAnswer":121},"How is distance traveled determined over a given time interval?",{"text":122,"@type":114},"Distance traveled is computed from the magnitude of the position changes (using where the motion reverses). Over the interval, add the lengths of movement regardless of direction.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522865,1791775356,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},687207412472,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Calculus Name   \nMotion Along a Line Date  Period   \nA particle moves along a horizontal line. Its position function is s(t) for t ≥ 0. For each problem, find the velocity function v(t) and the acceleration function a(t). You may use the blank graphs to sketch s(t), v(t), and a(t).  \n1) s(t) = t3 − t2 − 56t  \n600  \n400  \n200  \n−200  \n−400  \n−600  \n\n|  s(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | 2 |  | 4 |  | 6 |  |  | 8 | 1 | 0 | 1 | 2 | 1 | 4 | 1 | 6 t |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n200  \n150  \n100  \n50  \n−50  \n−100  \n−150  \n−200  \n|  a(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | 2 |  | 4 |  | 6 |  |  | 8 | 1 | 0 | 1 | 2 | 1 | 4 | 1 | 6 t |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nA particle moves along a horizontal line. Its position function is s(t) for t ≥ 0. For each problem, find the displacement of the particle and the distance traveled by the particle over the given interval. You may use the blank graph to sketch s(t).  \n2) s(t) = −t2 + 6t + 27; 0 ≤ t ≤ 4  \n120  \n80  \n40  \n−40  \n−80  \n−120  \n\n|  s(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | 2 |  | 4 |  | 6 |  |  | 8 | 1 | 0 | 1 | 2 | 1 | 4 | 1 | 6 t |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n3) s(t) = −t3 + 11t2 ; 3 ≤ t ≤ 8  \n600  \n400  \n200  \n−200  \n−400  \n−600  \n\n|  s(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  ","cbCaicXNrO1j6fZk","https://ap.wps.com/l/cbCaicXNrO1j6fZk","pdf",56383,"English","# Problems\n## Kinematics from s(t)\n## Displacement and distance traveled\n## Maximum speed and direction changes\n## Acceleration zero points and speeding/slowing intervals","[{\"question\":\"How are velocity v(t) and acceleration a(t) obtained from the position function s(t)?\",\"answer\":\"Velocity is found by differentiating s(t) with respect to t, and acceleration is found by differentiating v(t) (equivalently, differentiating s(t) twice).\"},{\"question\":\"What does the worksheet ask for besides v(t) and a(t) in the direction-change problems?\",\"answer\":\"It requires the times when the particle changes directions, the intervals when it moves left versus right, the times when acceleration equals 0, and the intervals when the particle is slowing down or speeding up.\"},{\"question\":\"How is distance traveled determined over a given time interval?\",\"answer\":\"Distance traveled is computed from the magnitude of the position changes (using where the motion reverses). Over the interval, add the lengths of movement regardless of direction.\"}]","Motion Along a Line - Problem Set - Velocity, Acceleration, and Displacement | PDF",1791426249]