constant acceleration equations - nuffield恒定加速度方程纳菲尔德

《constant acceleration equations - nuffield恒定加速度方程纳菲尔德》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、AResourceforFree-standingMathematicsQualificationsConstantAccelerationEquationsAccelerationAccelerationistherateofchangeofvelocityofamovingobject.Itisusuallymeasuredin'metrespersecondsquared',whichisabbreviatedtoms-2.Anaccelerationof2ms-2meansthatthevelocityoftheobjectisincr

2、easingby2metrespersecondeverysecond.Ifthevelocityoftheobjectisdecreasingby2metrespersecondeverysecond,thentheaccelerationis–2ms-2.Thisiscalleddecelerationorretardation.Likevelocity,accelerationisavector,havingbothdirectionandmagnitude.(Noteanegativesignmayalsoindicatetheobje

3、ctisspeedingupinthenegativedirection.)Velocity-timegraphsAccelerationThegradientofthevelocity-timegraphofamovingobjectgivesitsacceleration.vms-1tseconds0205Ifthegraphisastraightlinetheaccelerationisconstant.ExampleThisgraphshowsthevelocityofacarthatacceleratesataconstantrate

4、from0to20ms-1in5seconds.Thecar'sacceleration==4ms-2Youmayknowthattheareaunderavelocity-timegraphgivesthedisplacementordistancemoved.Inthiscasethedistancemoved==50mThefactsyoumayneedinthefollowingworkaresummarisedbelow.Usethemonthenextpagetoderiveanimportantsetofequationsthat

5、applywhenobjectsmovewithconstantacceleration.Theseequationscanbeusedtomodelmanyreal-lifesituations.SummaryGradientofavelocity-timegraph==accelerationAreaunderavelocity-timegraph=displacementAreaofatriangle==Areaofatrapezium==bhbhavt0dtdv©TheNuffieldFoundationPhoto-copiable3A

6、ResourceforFree-standingMathematicsQualificationsConstantAccelerationEquationsConstantAccelerationEquationsvuVelocityTime0tThisvelocity-timegraphshowsthevelocityofanobjectincreasingfromaninitialvalue,u,toafinalvalue,v,intimet.Workthroughthefollowingstepstoderivetheequations.

7、a=Writedownanexpressionfortheacceleration,a,intermsofu,vandt.……………………………………………….........Rearrangethisequationtomakethesubjectv.……………………………………………………..……………………………………………………..v=…..………………………………………………(1)Usetheareaunderthegraphtowriteanexpressionforthedisplacement,s,intermsofu,vand

8、t.s=….………………………………………………(2)Substitutetheexpressionforvfromequation(1)intoeq