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The problems require sketching momentum and energy graphs, deriving an equation for the spring constant from conservation of energy, comparing speeds at specified positions using energy curves, and proposing procedures with uncertainty reduction and data analysis via linear graph slope.",{"@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/ap-physics-1-algebra-based-2025-free-response-questions-question-1-3/459195/",{"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/ap-physics-1-algebra-based-2025-free-response-questions-question-1-3/459195.png","ImageObject",300,407,{"name":92,"@type":93},"Aldword","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is momentum graphically analyzed in Question 1?","Question",{"text":112,"@type":113},"Sketch the magnitude of the x-component of momentum as a function of time from t=0 until after the collision completes. Use the collision and sticking behavior to determine how momentum changes over time.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What principle is used to derive the spring constant in Question 2?",{"text":117,"@type":113},"Use conservation of energy between the block’s initial release position and the moment when it comes to rest at maximum spring compression, expressing the result in terms of M, θ, D, and physical constants as needed.",{"name":119,"@type":110,"acceptedAnswer":120},"How can students determine an unknown block mass in Question 3?",{"text":121,"@type":113},"Collect measurements from the meterstick and spring scale setup to create a linear graph where the slope depends on the block’s mass, then analyze the slope to determine mo while including steps to reduce experimental uncertainty.","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},459195,1790755429,{"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":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"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":129,"read_time":143,"preview_page_count":4},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","APPHYSICS 1:ALGEBRA-BASED 2025·FREE-RESPONSE QUESTIONS  \n# Question 1:VersionJ\n\n1.Astudent has a cart of mass m。and a block of mass  \n,as shown in Figure 1.  \n·At time r=0,the cart is moving to the rightacross a horizontal surface with constant  \nspeed ve,and the student releases the block from rest.  \n·Atr=l,the block collides with and sticks to the top of the cart.The blnck dnes not slide  \non the cart.  \n·Atr=L₂,the block-cart system continuesto move to the right with constant speed vy.  \nFigure 1  \nBlock.  \n\n| A.  \u003Cbr>i.On the axes sho  \u003Cbr>of the momentu  \u003Cbr>●2025Clege Board.  \u003Cbr>Mst CalegeEoard onte web:coleg   | ¥t  \u003Cbr>wn in Figure 2,sketch a graph of the magnitude p,of the x-component  \u003Cbr>m of the block-cartsystem as a function of time t fromt=0until r>2.   |\n| --- | --- |\n|  |  |\n|  | Figure 2  \u003Cbr>3  \u003Cbr>eboardaorn   |\n\ni.  \niⅢ  \nInformaton.  \nB.Consider the case where a new blockis dropped and collides withnew block slides along the cart during the collision but does not sliinterval from when the new block collides with the cart and movesis Ar.During △r there is a frictionalforce between the new block a  \nIndicatewhether thex-component ofthe momentum of the newrdecreases,or remains constant during Ar.  \n—__Increases  \nDecrease  \n√Remains constant  \nF4+=0  \nJustifyyour response  \nkinetic  \n→△e  \nr:A\\  \nAtx~  \n*-dctm  \nConse r  \n62025Colage Boed  \nVat Cclge Bordonthewen odegboardarg  \np。=Pf  \n55  \nQuestion 2:Version J  \n2.Ablock of mass Mis released from rest at position x=0 near the top of a ramp.The rampmakes an angle of θ with the horizontal.The block slides down the ramp with negligiblefriction.AL x=8D the block makes contact with an uncompressed spring with springconstant k.The spring is then compressed and the block momentarily comes to rest at x=12D,Figure 1 shows the instants when the block is at x=0,x=6D,and x=10D,respectively.  \nA.Figure 4 shows an energy bar chart that represents the kinetic energy K of the block,thegravitational potential energyU,of the block-spring-Earth svstem,and the spring potentialenergy U,of the block-spring-Earth system at the instant that the block is at x=10D.Thegravitational potential energy U,of the block-spring-Earth system is defined to be zero whenthe block momentarily comes to rest at x=12D.  \nDraw shaded bars that represent K,U,and U,to complete the energy bar charts inFigure 2 and Figure 3 for when the block is released from rest atx=0 and for when theblock is at x=6D,respectively.  \n·Shaded hars should start at the dashed line that represents zer energy.  \n·Represent any energy that is equal to zero with a distinct line on the zero-energy line.  \n·The relative heights ofeach shaded bar should reflect the magnitude of the respectiveenergy consistent with the scale used in Figure 4,  \nx=6Dx=10D  \n2E。一EFigure 2Figure 3Figure 4  \n2025CollegeBoard.  \nVist Colege Board on theweb;collegeboard.org  \nB.Figure 5shows the block at x=0when the block is released from rest and the block atx=12D when the block momentarily comes to rest against the compressed spring.  \nFigure 5  \nStarting with conservation of energy,derive an equation for the spring constant k.Expressyour answer in terms of M,θ,D,and physical constants,as appropriate.Begin yourderivation by writing a fundamental physics principle or an equation from the referenceinformation.  \nC.Figure 6 shows a graph of the energy of the system asa function of the position of the blockfrom x=8D tox=12D.The spring potential energy U,of the block-spring-Earth system isshown on the graph.  \nOn the axes shown in Figure6,do the following.  \ni.Sketch and label a line or curve that represents the total mechanical energy E for theblock-spring-Earth system as a function of the position of the block from x=8Dto x=12D,  \n   \n   \nii.Sketch and label a line or curve that represents the gravitational potential energy U,forthe block-spring-Earth system as a function of the poition of the block fromx=8Dto x=12D,  \nFigure 6  \n●2025ColegeBoard.  \nVst","cbCaikMrsOte54gG","https://ap.wps.com/l/cbCaikMrsOte54gG","pdf",5225182,"English","# Question 1\n## Momentum vs. time after a collision\n## Momentum change with a new block during collision\n# Question 2\n## Energy bar charts at specified positions\n## Derive spring constant using conservation of energy\n## Sketch total and gravitational energy curves vs. position\n## Compare block speeds at specified positions\n# Question 3\n## Experimental procedure to determine unknown block mass\n## Graphing and analyzing the linear relationship","[{\"question\":\"How is momentum graphically analyzed in Question 1?\",\"answer\":\"Sketch the magnitude of the x-component of momentum as a function of time from t=0 until after the collision completes. Use the collision and sticking behavior to determine how momentum changes over time.\"},{\"question\":\"What principle is used to derive the spring constant in Question 2?\",\"answer\":\"Use conservation of energy between the block’s initial release position and the moment when it comes to rest at maximum spring compression, expressing the result in terms of M, θ, D, and physical constants as needed.\"},{\"question\":\"How can students determine an unknown block mass in Question 3?\",\"answer\":\"Collect measurements from the meterstick and spring scale setup to create a linear graph where the slope depends on the block’s mass, then analyze the slope to determine mo while including steps to reduce experimental uncertainty.\"}]","AP Physics 1 - Algebra-Based 2025 Free-Response Questions - Question 1-3 | PDF",18]