[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572828-105":53,"doc-detail-572828-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","kinematics-cheat-sheet-vector-vs-scalar-kinematics-equations","Kinematics Cheat Sheet - vector vs. scalar - kinematics equations","","Kinematics Cheat Sheet provides compact definitions and formulas for describing motion using scalars and vectors, including reference frame conventions and sign choices. It summarizes key quantity types such as displacement, position, speed, velocity, and acceleration with corresponding units and guidance for determining them from equations and graphs. The sheet also includes constant-velocity graph interpretations, displacement relationships, and worked examples that compute displacement, average velocity, and meeting time/position for moving objects.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/kinematics-cheat-sheet-vector-vs-scalar-kinematics-equations/572828/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/kinematics-cheat-sheet-vector-vs-scalar-kinematics-equations/572828.png","ImageObject",442,249,{"name":88,"@type":89},"adawds","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":73},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What is the difference between vector and scalar quantities in this cheat sheet?","Question",{"text":108,"@type":109},"Scalar quantities are described completely by magnitude, while vectors require both magnitude and direction. The cheat sheet uses this distinction when defining motion-related quantities like displacement/velocity versus speed/other scalars.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do you determine displacement, speed, and direction from a constant-velocity graph?",{"text":113,"@type":109},"The cheat sheet states that displacement comes from the area under the curve, speed corresponds to the absolute value of the slope, and direction comes from the sign of the slope. Velocity is taken as the slope and initial position is read directly as x₀.",{"name":115,"@type":106,"acceptedAnswer":116},"How do you find when two cars moving toward each other meet?",{"text":117,"@type":109},"Write position equations for each car as functions of time using their starting positions and velocities, then set the positions equal and solve for time. The cheat sheet’s example also asks for the meeting position after solving for time.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},572828,1792497849,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":73,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":79,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":73},3985747872983,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Kinematics Cheat Sheet  \n| Vector vs.Scalar  \u003Cbr>Scalar-a quantity that is described completely by  \u003Cbr>its size(magnitude)  \u003Cbr>Vector-a quantity that requires both a magnitude  \u003Cbr>and direction to be completely described   | Reference Frame  \u003Cbr>To describe motion unambiguously,we need to  \u003Cbr>define  \u003Cbr>2.posifive  \u003Cbr>By convention,norHh  ___and  \u003Cbr>____are defined as positive  \u003Cbr>directions(usually)  \u003Cbr>east  \u003Cbr>clock  \u003Cbr>negahive direchon  \u003Cbr>. origin   |\n| --- | --- |\n| Definition:  \u003Cbr>Formula:  \u003Cbr>Where △x is  \u003Cbr>and x is  \u003Cbr>And x₀is  \u003Cbr>Type of quantity:Vector  \u003Cbr>Sl units:  \u003Cbr>Sketch:  \u003Cbr>。  \u003Cbr>△X  \u003Cbr>X  \u003Cbr>meter  \u003Cbr>displacement  \u003Cbr>△x=×-X。  \u003Cbr>Pbšihon  \u003Cbr>changn noljects   | How to find:  \u003Cbr>Type of quantity:  \u003Cbr>步units:  \u003Cbr>Sketch:  \u003Cbr>di stance is alwauys  \u003Cbr>posifive!  \u003Cbr>Xo  \u003Cbr>X  \u003Cbr>melers,  \u003Cbr>miles, km,erc.  \u003Cbr>scalour  \u003Cbr>add up tho pat  \u003Cbr>has overed in its mohon  \u003Cbr>How much groond.an object   |\n| Formula:  \u003Cbr>Type of quantity:scolor  \u003Cbr>S units:  \u003Cbr>Notes:  \u003Cbr>speed is always  \u003Cbr>posihve!.  \u003Cbr>mi/hr,  \u003Cbr>/  \u003Cbr>km/  \u003Cbr>moving·  \u003Cbr>Hou fast an object is   | Formula:  \u003Cbr>Sl units:  \u003Cbr>No  \u003Cbr>i dis  \u003Cbr>/  \u003Cbr>Position.  \u003Cbr>t a  an objec ch   |\n\n| Acceleration  \u003Cbr>,in velocihy  \u003Cbr>ouer  \u003Cbr>Definition:  \u003Cbr>ime  \u003Cbr>Formula:  \u003Cbr>=  \u003Cbr>or  \u003Cbr>Sl units:  \u003Cbr>Spe   | Kinematics Equations  \u003Cbr>.  \u003Cbr>V =Vo +at  \u003Cbr>.  \u003Cbr>.  \u003Cbr>4.  \u003Cbr>Wher  \u003Cbr>xis  \u003Cbr>xo is inihial posihon  \u003Cbr>v is final velociby  \u003Cbr>vo is(nihial velocihy  \u003Cbr>a is accelerahon  \u003Cbr>t is time   |\n| --- | --- |\n| From the graph you can find  \u003Cbr>·Displacement(△x)  \u003Cbr>·Speed (absolute value of the slope)  \u003Cbr>·Direction (sign of the slope)  \u003Cbr>·Velocity (slope)  \u003Cbr>·Initial position(x。)   | graphs for constant velocity-examples  \u003Cbr>X  \u003Cbr>X  \u003Cbr>七  \u003Cbr>negative   |\n| Vvs.t graph(constant velocity  \u003Cbr>·Area under the curve gives displacement  \u003Cbr>(△x)   |  |\n\n七  \n七  \nExamples 1&2:  \n\n| Object   | Initial Position xo   | Final Position x   | Time   |\n| --- | --- | --- | --- |\n| A   | +2.0 m   | +6.0m   | 0.5s   |\n| B   | +6.0 m   | +2.0m   | 0.5 s   |\n| C   | -3.0m   | +7.0m   | 0.5s   |\n\nFind the displacement of each object(magnitude and direction+/-):  \n△x= X一Xo  \nA△x=+6m- 2m 三 +4m  \nB!=2m一m二一4m  \n7m-(-3m)=十io m△x=C:  \nch object(magnitude and direction+/-):  \n3.Andy Green in the car ThrustSSC set a world record of 341.1 m/s in 1997.The car waspowered by two jet engines,and it was the first one officially to exceed the speed of sound.Toestablish such a record,the driver makes two runs through the course,one in each direction tonullify wind effects.The car first travels from left to right and covers a distance of 1609m in atime of 4.740s.In the reverse direction,the car covers the same distance in 4.695s.Determinethe average velocity for each run.Vz十  \nSketch:  \nFinish  \nSfart  \nInventory of known quantities:△x,= +1L09m△x=-i609 m七,=4.740st2= 4.695s  \nRun 1(Left to right):  \nRun 2(Right to left):  \n4.Two toy cars are placed 10 meters apart on a track.The red car is placed at the origin andmoves to the right at a speed of 1.2 m/s.The blue car is placed at the+10m mark and moves tothe left at a speed of 3.1 m/s.At what time will the two cars meet?At what position willthe twocars meet?V=-3.|  \n!一2  \nSketch:  \nd  \niOm  \nihre  mee  \n1.2  \nred car:d二 0+互t  \nblue uar!d=10m+(-3.1m人)t  \n=iOm-3.I七  \n1.2  \n七=|C七4.3  \nc 2.33 sec.  \n二  \n1.m.3)  \n2年(2  \n=、m  \n5.(Giancoli\\#5)You are driving home from school steadily at 65mph for 130 miles.It then  \nd=203.2mi= 2hcfor segmen+2:for segment 1:Homeschcool七七OmiV=6SmphV=Ss mph  \n(a)How far is your hometown from school?  \n(b)What was your average speed?","cbCaim2Fhk5l4Nkr","https://ap.wps.com/l/cbCaim2Fhk5l4Nkr","pdf",1294022,"English","# Vector vs. Scalar\n## Reference Frame\n# Definitions and Formulas\n## Displacement, Speed, Velocity, Acceleration\n# Kinematics Equations\n## V = Vo + at\n# Graph Interpretation\n## Constant Velocity Graphs\n# Worked Examples\n## Displacement with sign\n## Average velocity from runs\n## Two-car meeting problem","[{\"question\":\"What is the difference between vector and scalar quantities in this cheat sheet?\",\"answer\":\"Scalar quantities are described completely by magnitude, while vectors require both magnitude and direction. The cheat sheet uses this distinction when defining motion-related quantities like displacement/velocity versus speed/other scalars.\"},{\"question\":\"How do you determine displacement, speed, and direction from a constant-velocity graph?\",\"answer\":\"The cheat sheet states that displacement comes from the area under the curve, speed corresponds to the absolute value of the slope, and direction comes from the sign of the slope. Velocity is taken as the slope and initial position is read directly as x₀.\"},{\"question\":\"How do you find when two cars moving toward each other meet?\",\"answer\":\"Write position equations for each car as functions of time using their starting positions and velocities, then set the positions equal and solve for time. The cheat sheet’s example also asks for the meeting position after solving for time.\"}]","Kinematics Cheat Sheet - vector vs. scalar - kinematics equations | PDF",1791929427]