[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-315591-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-315591-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","unit-3-aos-1-formula-sheet-motion","Unit 3 AOS 1 Formula Sheet - Motion","","Unit 3 AOS 1 Formula Sheet - Motion collects key physics relationships covering motion, circular motion, projectiles, and Newton’s laws. It summarizes constant-acceleration equations, centripetal quantities, banking track geometry, and conditions for maintaining contact. The sheet also links force, energy, and mass through Hooke’s law, elastic, kinetic and gravitational potential energy, momentum and impulse, and conservation principles. It includes work and power formulas, collision energy relations, plus unit 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equations are provided for constant acceleration problems?","Question",{"text":63,"@type":64},"The sheet lists the standard constant-acceleration relationships linking velocity, initial velocity, acceleration, time, displacement, and final velocity.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which formulas relate centripetal force and centripetal acceleration in circular motion?",{"text":68,"@type":64},"It includes centripetal force and centripetal acceleration relationships, using mass, velocity, radius, and period.",{"name":70,"@type":61,"acceptedAnswer":71},"How are energy, momentum, and impulse connected on the sheet?",{"text":72,"@type":64},"It provides formulas for elastic potential energy, kinetic energy, gravitational potential energy, momentum, and impulse, including conservation of momentum and work done.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},315591,1789905329,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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= 9.81 m s −2 |\n| --- | --- |\n\nNewton’s laws of motion  \n\n| Velocity; acceleration (vectors) | 􀝒 = 􀯫􀯧; 􀜽 = |  |  |  | ∆􀯩∆􀯧 | ∆􀝔 = s = displacement/change in position (m)\u003Cbr>∆􀝐 = time (s)\u003Cbr>􀝒 = velocity (m s-1)\u003Cbr>∆􀝒 = change in velocity (m s-1)\u003Cbr>􀜽 = acceleration (m s-2) |\n| --- | --- | --- | --- | --- | --- | --- |\n| Equations for constant acceleration | 􀝒 = 􀝑 + 􀜽􀝐\u003Cbr>􀝏 = 􀝑􀝐 + 12 􀜽􀝐2\u003Cbr>􀝏 = 􀝒􀝐 − 12 􀜽􀝐2\u003Cbr>􀝒 2 = 􀝑 2 + 2􀜽􀝏 1\u003Cbr>􀝏 = (􀝑 + 􀝒)􀝐 2 |  |  |  |  | 􀝒 = final velocity (m s-1)\u003Cbr>􀝑 = initial velocity (m s-1)\u003Cbr>􀜽 = acceleration (m s-2)\u003Cbr>􀝏 = displacement (m)\u003Cbr>􀝐 = time (s) |\n| Newton’s second law | 􀜨􀯡􀯘􀯧 = 􀝉􀜽 |  |  |  |  | 􀜨􀯡􀯘􀯧 = net force (N)\u003Cbr>􀝉 = mass (kg)\u003Cbr>􀜽 = acceleration (m s-2) |\n| Period of object moving in a circular path* | 􀜶 = 1􀝂 |  |  |  |  | 􀜶 = period (s)\u003Cbr>􀝂 = frequency (Hz or s-1) |\n| Velocity of object moving in a circular path | 􀝒 = |  | 2􀟨􀝎􀜶 |  |  | 􀝒 =velocity (m s-1)\u003Cbr>􀝎 = radius (m)\u003Cbr>􀜶 = period (s) |\n| Centripetal force | 􀜨􀯡􀯘􀯧 = | 􀝉􀝒2 4􀟨2􀝎􀝉\u003Cbr>~~ ~~ = ~~ ~~\u003Cbr>􀝎 􀜶 2 |  |  |  | 􀜨􀯡􀯘􀯧 = net force/centripetal force (N)\u003Cbr>􀝉 = mass (kg)\u003Cbr>􀝒 =velocity (m s-1)\u003Cbr>􀝎 = radius (m)\u003Cbr>􀜶 = period (s) |\n| Centripetal acceleration* | 􀝒 2 4􀟨2􀝎\u003Cbr>􀜽 = ~~ ~~ = ~~ ~~􀝎 􀜶 2 |  |  |  |  | 􀜽 = centripetal acceleration (m s-2)\u003Cbr>􀝒 =velocity (m s-1)\u003Cbr>􀝎 = radius (m)\u003Cbr>􀜶 = period (s) |\n| Angle of banked track* | tan (􀟠) = |  |  | 􀝒 2\u003Cbr>􀝎􀝃 |  | 􀟠 = banking angle from horizontal (°)\u003Cbr>􀝒 = velocity (m s-1)\u003Cbr>􀝎 = radius (m) |\n| Design speed of banked track* | 􀝒 = √􀝎􀝃􀝐􀜽􀝊 (􀟠) |  |  |  |  | 􀝒 = velocity (m s-1)\u003Cbr>􀝎 = radius (m)\u003Cbr>􀟠 = banking angle from horizontal (°) |\n| Minimum velocity (top, inside circle) or maximum velocity (top, outside circle) to stay in contact with track* | 􀝒 = √􀝎􀝃 |  |  |  |  | 􀝒 = velocity (m s-1)\u003Cbr>􀝎 = radius (m) |\n| Range of projectile with symmetrical trajectory* | 􀜴 = 􀝑~~ ~~2~~ ~~sin􀝃(2􀟠) |  |  |  |  | 􀜴 = range/horizontal displacement (m)\u003Cbr>􀝑 = initial velocity (m s-1)\u003Cbr>􀟠 = angle of firing above horizontal (°) |\n\nRelationships between force, energy and mass  \n\n| Hooke’s Law (springs) | 􀜨􀯦 = −􀝇∆􀝔 Note: negative sign denotes direction |  | 􀜨􀯦 = force by the spring (N)\u003Cbr>􀝇 = spring constant (N m-1)\u003Cbr>∆􀝔 = change in spring length by extension or compression (m) |\n| --- | --- | --- | --- |\n| Elastic potential energy | 􀜧􀯦 = 12 􀝇∆􀝔2\u003Cbr>OR: area under force-extension (or forcecompression) graph |  | 􀜧􀯦 = elastic potential energy (J)\u003Cbr>􀝇 = spring constant (N m-1)\u003Cbr>∆􀝔 = change in spring length by extension or compression (m) |\n| Kinetic energy | 􀜧􀯞 = 12 􀝉􀝒2 |  | 􀜧􀯞 = kinetic energy (J)\u003Cbr>􀝉 = mass (kg)\u003Cbr>􀝒 = speed (m s-1) |\n| Gravitational potential energy | 􀜧􀯚 = 􀝉􀝃∆ℎ\u003Cbr>Note: only use when close to Earth’s surface, where 􀝃 can be considered a constant. |  | 􀜧􀯚 = gravitational potential energy (J)\u003Cbr>􀝉 = mass (kg)\u003Cbr>∆ℎ = change in vertical height (m) |\n| Momentum (vector) | 􀝌 = 􀝉􀝒 |  | 􀝌 = momentum (kg m s-1)\u003Cbr>􀝉 = mass (kg)\u003Cbr>􀝒 = velocity (m s-1) |\n| Impulse (vector) | 􀜫 = ∆􀝌 = 􀝉∆􀝒 = 􀜨􀯔􀯩 ∆􀝐 OR: area under force-time graph |  | 􀜫 = impulse (N s)\u003Cbr>∆􀝌 = change in momentum (m s-1)\u003Cbr>􀝉 = mass (kg)\u003Cbr>∆􀝒 = change in velocity (m s-1)\u003Cbr>􀜨􀯔􀯩 = average force (N)\u003Cbr>∆􀝐 = time (s) |\n| Conservation of momentum* | ∑ 􀝌􀯜 = ∑ 􀝌􀯙\u003Cbr>Two objects colliding and remaining separate:\u003Cbr>􀝉1􀝑1 + 􀝉2􀝑2 = 􀝉1 􀝒1 + 􀝉2􀝒2 Two objects colliding and joining together:\u003Cbr>􀝉1􀝑1 + 􀝉2􀝑2 = (􀝉1 + 􀝉2)􀝒 |  | ∑ 􀝌􀯜 = sum of initial momenta (kg m s-1)\u003Cbr>∑ 􀝌􀯙 = sum of final momenta (kg m s-1)\u003Cbr>􀝒 = final velocity (m s-1)\u003Cbr>􀝑 = initial velocity (m s-1)\u003Cbr>􀝉 = mass (kg) |\n| Work done* | 􀜹 = ∆􀜧 = 􀜨􀝏􀜿􀝋􀝏 (􀟠) Note: only use if force is constant\u003Cbr>OR: area under force-distance graph (if force not constant) |  | 􀜹 = work done (J)\u003Cbr>∆􀜧 = change in energy (J)\u003Cbr>􀜨 = force (N)\u003Cbr>􀝏 = displacement (m)\u003Cbr>􀟠 = angle between displacement and force (°) |\n| Power* | 􀜲 = | 􀜹\u003Cbr>􀝐 | 􀜲 = power (W)\u003Cbr>􀜹 = work done (J)\u003Cbr>􀝐 = time (s) |","cbCaihxolubWTTVk","https://ap.wps.com/l/cbCaihxolubWTTVk","pdf",232594,"English","# Motion constants and Newton’s laws\n## Circular motion and banking track\n## Projectile range\n## Force, energy and mass relationships\n## Unit conversions","[{\"question\":\"What equations are provided for constant acceleration problems?\",\"answer\":\"The sheet lists the standard constant-acceleration relationships linking velocity, initial velocity, acceleration, time, displacement, and final velocity.\"},{\"question\":\"Which formulas relate centripetal force and centripetal acceleration in circular motion?\",\"answer\":\"It includes centripetal force and centripetal acceleration relationships, using mass, velocity, radius, and period.\"},{\"question\":\"How are energy, momentum, and impulse connected on the sheet?\",\"answer\":\"It provides formulas for elastic potential energy, kinetic energy, gravitational potential energy, momentum, and impulse, including conservation of momentum and work done.\"}]","Unit 3 AOS 1 Formula Sheet - Motion | PDF"]