[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522929-105":59,"doc-detail-522929-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","motion-along-a-line-revisited-worksheet-problems-1-4","Motion Along a Line Revisited - Worksheet - Problems 1-4","","Worksheets on one-dimensional particle motion using velocity and acceleration functions for t ≥ 0. Problems ask for position s(t) from a given v(t), and for both s(t) and v(t) from a given acceleration a(t), including using initial conditions such as s(0) = 0 and v(0) = 0. Other questions require evaluating position, velocity, speed, and acceleration at a specified time, and computing displacement and distance traveled over a given interval.",{"@graph":69,"@context":122},[70,84,105],{"@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-revisited-worksheet-problems-1-4/522929/",{"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-revisited-worksheet-problems-1-4/522929.png","ImageObject",300,407,{"name":92,"@type":93},"นรินทร์","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the position function s(t) from a given velocity function v(t)?","Question",{"text":112,"@type":113},"Integrate v(t) to obtain s(t), then use the initial condition s(0) (or other provided position condition) to determine the constant of integration.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"If the acceleration function a(t) is given, how are s(t) and v(t) determined?",{"text":117,"@type":113},"Integrate a(t) to get v(t), apply the initial velocity condition such as v(0), then integrate v(t) to obtain s(t) and use s(0) to set the constant.",{"name":119,"@type":110,"acceptedAnswer":120},"How are displacement and distance traveled computed over a time interval?",{"text":121,"@type":113},"Displacement comes from the net change in position over the interval. Distance traveled uses the total accumulated magnitude of velocity (or speed) over the same time range.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522929,1791506094,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},2336475104957,"https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136","Kuta Software-Infinite Calculus Name   \nMotion Along a Line Revisited Date  Period   \nA particle moves along a coordinate line. Its velocity function is v(t) for t ≥ 0. For each problem, find the position function s(t). You may use the blank graphs to sketch s(t) and v(t).  \n1) v(t) = 3t2 − 22t; s(0) = 0  \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\n160  \n120  \n80  \n40  \n−40  \n−80  \n−120  \n−160  \nv(t)  \n2 4 6 8 10 12 14 16 t  \nA particle moves along a coordinate line. Its acceleration function is a(t) for t ≥ 0. For each problem, find the position function s(t) and the velocity function v(t). You may use the blank graphs to sketch s(t), v(t), and a(t).  \n2) a(t) = −12t2 + 60t; s(0) = 0; v(0) = 0  \n4000  \n3000  \n2000  \n1000  \n−1000  \n−2000  \n−3000  \n−4000  \n\n|  s(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\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|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n1000  \n800  \n600  \n400  \n200  \n−200  \n−400  \n−600  \n−800  \n−1000  \n\n|  v(t) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\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\n300  \n250  \n200  \n150  \n100  \n50  \n−50  \n−100  \n−150  \n−200  \n−250  \n−300  \na(t)  \n2 4 6 8 10 12 14 16 t  \nA particle moves along a coordinate line. Its acceleration function is a(t) for t ≥ 0. For each problem, find the position, velocity, speed, and acceleration at the given value for t. You may use the blank graphs to sketch s(t), v(t), and a(t).  \n3) a","cbCaiq0cjJ6xZvfj","https://ap.wps.com/l/cbCaiq0cjJ6xZvfj","pdf",53712,"English","# Motion Along a Line Revisited\n## Velocity-to-Position Problems\n## Acceleration-to-Position and Velocity Problems\n## Evaluation at a Given Time\n## Displacement and Distance Traveled","[{\"question\":\"How do you find the position function s(t) from a given velocity function v(t)?\",\"answer\":\"Integrate v(t) to obtain s(t), then use the initial condition s(0) (or other provided position condition) to determine the constant of integration.\"},{\"question\":\"If the acceleration function a(t) is given, how are s(t) and v(t) determined?\",\"answer\":\"Integrate a(t) to get v(t), apply the initial velocity condition such as v(0), then integrate v(t) to obtain s(t) and use s(0) to set the constant.\"},{\"question\":\"How are displacement and distance traveled computed over a time interval?\",\"answer\":\"Displacement comes from the net change in position over the interval. Distance traveled uses the total accumulated magnitude of velocity (or speed) over the same time range.\"}]","Motion Along a Line Revisited - Worksheet - Problems 1-4 | PDF",1791426316]