[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207811-en":3,"doc-seo-207811-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207811,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",4,"Exam","Physics - Using S.I. units","Worksheet focuses on using S.I. units to solve physics problems and verify equation correctness through unit homogeneity. It introduces base quantities and derived quantities, showing how derived unit expressions come from base units. Learners practise working out missing units and unit symbols in a table, calculating units through equations, and checking whether both sides of key formulas match in overall units. Activities include speed, kinetic energy, charge, power, and gravitational field strength.","Using S.I. units  \nSpecification references  \n• 2.1.2 a) b) c) d)  \n• M0.1 Recognise and make use of appropriate units in calculations  \nLearning outcomes  \nAfter completing the worksheet you should be able to:  \n• show knowledge and understanding of base and derived S. I. units  \n• use equations to work out derived units  \n• use base units to check homogeneity of equations.  \nIntroduction  \nBase quantities are measured in base units. These are units that are not based on other units. For example, mass is measured in kilograms and length is measured in metres. Other quantities have units which are derived from the base quantities. For example, the unit of density (kg m–3) is derived from the kilogram and the metre.  \nThe first example shows you how to use an equation to work out the unit of a derived quantity. The second example shows you how to check that an equation is homogeneous or, in other words, that its units are balanced.  \nWorked example  \nQuestion  \nWhat is the S. I. unit of speed?  \nAnswer  \nStep 1  \nIdentify the equation to use.  \nSpeed is defined as: distatinceme~~ ~~ttravakeenlled Step 2  \nWrite the equation in terms of units.  \nThe S.I. unit of speed is defined as: unit~~ ~~ofunidtistaof~~ ~~tinceme~~ ~~ttraakveenlled Step 3  \nSelect the appropriate S. I. base units.  \nS. I. unit of distance = metre (m)  \nS. I. unit of time = second (s)  \nStep 4  \nInsert the S. I. base units into the equation.  \n metre (m)   \nS. I. unit of speed = = metre per second = m s–1 time taken (s)  \nQuestion  \n1 Work out the missing units, unit symbols and names, equations, and quantities in  \nthis table. (1 mark for each correct answer)  \n\n| Physical quantity | Equation used | Unit | Derived unit symbol and name |\n| --- | --- | --- | --- |\n| frequency | 1\u003Cbr>time period | a | Hz hertz |\n| volume | length3 | b | – |\n| acceleration | velocity\u003Cbr>time | c | – |\n| force | mass 􀁵 acceleration | kg m s–2 | d |\n| work and energy | force 􀁵 distance | e | J joule |\n| voltage |  energy  electric charge | J C–1 | f |\n| electrical resistance | g | VA–1 | h |\n| momentum | mass 􀁵 velocity | i | – |\n| impulse | force 􀁵 time | j | – |\n| k | force\u003Cbr>area | l | Pa pascal |\n| m | n | kg m–3 | – |\n\nWorked example  \nQuestion  \nCheck that the equation: kinetic energy = 12 m v2 is homogeneous.  \nAnswer  \nMake sure you always state which side of the equation you are working on, left-hand side (LHS) or right-hand side (RHS) .  \nStep 1  \nStart with the LHS. The unit of kinetic energy is the joule. Change this to base units. LHS: J = N m = kg m s–2 􀁵 m = kg m2 s–2  \nStep 2  \nRepeat Step 1 for the RHS.  \nRHS: units of 12 m v2 are kg 􀁵 (m s–1)2 = kg m2 s–2  \n1  \n(The constant, , is a number with no units. )  \n2  \nStep 3  \nDon’t forget to write your conclusion.  \nLHS = RHS so the equation is homogeneous.  \nWe can’t tell that there is a 12 in the equation, so we cannot say that the equation is correct, only that it is homogeneous.  \nQuestions  \n2 Use base units to show the equation Q = I t for electric charge passing a point in  \ntime t, when the electric current is I, is homogeneous. (1 mark)  \n3 Use base units to show that the equation P = I V is homogeneous , where I is electric current, V is voltage, and P is power measured in watts (W) .  \n(Hint: 1 W = 1 J s–1) (2 marks)  \n4 The Earth’s gravitational field strength, g = 9.81 N kg–1 , is also sometimes given as the acceleration due to gravity , g = 9.81 m s–2. Show that these units are  \nequivalent. (1 mark)  \nMaths skills links to other areas  \nYou may also need to check equations are homogeneous wherever they are used in the specification – examples can be found in Chapter 3 Motion, and Topic 4.8 Density and pressure.  \nYou can also use this method to help you decide whether you have remembered an equation correctly.  \nHomogeneity of physical equations  \nSpecification references  \n• 2.1.2 a) b) d)  \n• M0. 1, M2.2  \nIntroduction  \nIn physics, all physical quantities are defined by mathematical relationships , ","cbCaihaq4vZWO9l6","https://ap.wps.com/l/cbCaihaq4vZWO9l6","pdf",607803,1,29,"English","en",105,"# Learning outcomes\n# Base and derived S.I. units\n## Worked example: unit of speed\n# Unit calculation practice table\n# Homogeneity of physical equations\n## Worked example: kinetic energy\n# Further homogeneity questions\n## Charge, power, and gravitational field strength\n# Background: the Système Internationale (S.I.)\n## Table 1: S.I. base units\n## Derived units from relationships","[{\"question\":\"What are base units and derived units in S.I. measurements?\",\"answer\":\"Base units measure quantities that are not defined using other units (e.g., mass in kilograms, length in metres). Derived units are formed from base units through physical relationships (e.g., density in kg m⁻³).\"},{\"question\":\"How can you find the S.I. unit of a derived quantity like speed?\",\"answer\":\"Use the defining equation for the quantity, then substitute the S.I. base units for each variable. Simplifying the result gives the derived unit (for speed, metres per second, m s⁻¹).\"},{\"question\":\"How do you check whether a physics equation is homogeneous?\",\"answer\":\"Write units on both sides of the equation, convert to base units where needed, and compare the overall units. If LHS units equal RHS units, the equation is homogeneous.\"}]","Physics - Using S.I. units | PDF",1788601220,73,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"physics-using-si-units","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/physics-using-si-units/207811/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-07","2026-09-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What are base units and derived units in S.I. measurements?","Question",{"text":75,"@type":76},"Base units measure quantities that are not defined using other units (e.g., mass in kilograms, length in metres). Derived units are formed from base units through physical relationships (e.g., density in kg m⁻³).","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How can you find the S.I. unit of a derived quantity like speed?",{"text":80,"@type":76},"Use the defining equation for the quantity, then substitute the S.I. base units for each variable. Simplifying the result gives the derived unit (for speed, metres per second, m s⁻¹).",{"name":82,"@type":73,"acceptedAnswer":83},"How do you check whether a physics equation is homogeneous?",{"text":84,"@type":76},"Write units on both sides of the equation, convert to base units where needed, and compare the overall units. 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