欢迎来到麦多课文档分享! | 帮助中心 海量文档,免费浏览,给你所需,享你所想!
麦多课文档分享
全部分类
  • 标准规范>
  • 教学课件>
  • 考试资料>
  • 办公文档>
  • 学术论文>
  • 行业资料>
  • 易语言源码>
  • ImageVerifierCode 换一换
    首页 麦多课文档分享 > 资源分类 > PPT文档下载
    分享到微信 分享到微博 分享到QQ空间

    Calculus.ppt

    • 资源ID:379250       资源大小:984KB        全文页数:26页
    • 资源格式: PPT        下载积分:2000积分
    快捷下载 游客一键下载
    账号登录下载
    微信登录下载
    二维码
    微信扫一扫登录
    下载资源需要2000积分(如需开发票,请勿充值!)
    邮箱/手机:
    温馨提示:
    如需开发票,请勿充值!快捷下载时,用户名和密码都是您填写的邮箱或者手机号,方便查询和重复下载(系统自动生成)。
    如需开发票,请勿充值!如填写123,账号就是123,密码也是123。
    支付方式: 支付宝扫码支付    微信扫码支付   
    验证码:   换一换

    加入VIP,交流精品资源
     
    账号:
    密码:
    验证码:   换一换
      忘记密码?
        
    友情提示
    2、PDF文件下载后,可能会被浏览器默认打开,此种情况可以点击浏览器菜单,保存网页到桌面,就可以正常下载了。
    3、本站不支持迅雷下载,请使用电脑自带的IE浏览器,或者360浏览器、谷歌浏览器下载即可。
    4、本站资源下载后的文档和图纸-无水印,预览文档经过压缩,下载后原文更清晰。
    5、试题试卷类文档,如果标题没有明确说明有答案则都视为没有答案,请知晓。

    Calculus.ppt

    1、Calculus,6.3 Rectilinear Motion,6.3 Rectilinear Motion,Vocabulary,Day 1: Rectilinear Motion Position function Velocity function Instantaneous velocity Day 2: Speed function Instantaneous speed Day 3 Acceleration Function Speeding up Slowing down,Rectilinear Motion,Motion on a line,Moving in a positi

    2、ve direction from the origin,Moving in a negative direction from the origin,Position Function,Horizontal axis: time Vertical Axis: position on a line,Moving in a positive direction from the origin,Moving in a negative direction from the origin,Position function: s(t) s = position (sposition duh!) t

    3、= time s(t)= position changes as time changes,Sketchpad Example,Example,Use the position and time graph to describe how the puppy was moving,Velocity,Rate position change vs time change Velocity can be positive or negative positive: going in a positive direction negative: going in a negative directi

    4、on,Velocity,Position,Velocity function,Velocity is the slope of the position function (change in position /change in time) velocity =Technically this is instantaneous velocity,Velocity,Rate at which a coordinate of a particle changes with time Insanities velocity s(t) = position with respect to time

    5、 Instantaneous velocity at time t is:,v(t) = positive increasing slope moving in a positive direction,v(t) = negative decreasing slope moving in a negative direction,Practice,Let s(t)= t3-6t2 be the position function of a particle moving along an s-axis were s is in meters and t is in seconds. Graph

    6、 the position function On a number line, trace the path that the particle took. Where will the velocity be positive? Negative? Graph the instantaneous velocity. Identify on the velocity function when the particle was heading in a positive direction and when it was heading in a negative direction.,Ve

    7、locity or Speed,Speed change in position with respect to time in any direction Velocity is the change in position with respect to time in a particular direction Thus Speed cannot be negative because going backwards or forwards is just a distance Thus Velocity can be negative because we care if we go

    8、 backwards,Speed,Absolute Value of Velocity,example: if two particles are moving on the same coordinate line with velocity of v=5 m/s and v=-5 m/s,then they are going in opposite directionsbut both have a speed of |v|=5 m/s,Example - s(t)= t3-6t2,time,speed,Practice,Graph the velocity function What

    9、will the speed function look like? At what time(s) was the particle heading in a negative direction? Positive direction?,Acceleration,the rate at which the velocity of a particle changes with respect to time. If s(t) is the position function of a particle moving on a coordinate line, then the instan

    10、taneous acceleration of the particle at time t isor,Example,Let s(t) = t3 6t2 be the position function of a particle moving along an s-axis where s is in meters and t is in seconds. Find the instantaneous acceleration a(t) and shows the graph of acceleration verses time,Day 3: Speeding Up & Slowing

    11、down,Speeding up when slope of speed is positive Slowing down when slope of speed is negative,Example,When is s(t) speeding up and slowing down?,speed,acceleration,Velocity & Acceleration function,Slowing down,Velocity +,Acceleration -,Speeding up,Velocity -,Acceleration -,Slowing down,Velocity -,Ac

    12、celeration +,Speeding up,Velocity +,Acceleration +,Analyzing Motion,Positive “s” values,Positive side of the number line,Negative side of the number line,Negative “s” values,s(t)=velocity.,Look for Critical Pts,Postive “v” values,0 “v” values (CP),Negative “v” values,Moving in + direction,Turning/st

    13、opped,Moving in a direction,v(t)=acceleration,Look for Critical Pts,+ a, + v = speeding up - a, - v = speeding up + a, - v = slowing down - a, + v = slowing down,Example,Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3 Analyze the motion

    14、of the particle for t0,Position,Velocity,Acceleration,Never 0 (t0), always postive,Always on postive side of number line,+,-,+,0,0,0t2 going pos direction,t=2 turning,2t5 going neg. direction,t=5 turning,t5 going pos. direction,t=0,t=2,t=5,+,-,-,+,-,-,+,+,0t2 slowing down,2t3.5 speeding up,3.5t5 slo

    15、wing down,5t speeding up,Example,Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3 Analyze the motion of the particle for t0,position,velocity,Acceleration,position,velocity,Acceleration,Position,Direction of motion,+,-,+,stop,stop,positiv

    16、e direction,negative direction,positive direction,v(t),+,-,+,7/2,a(t),-,+,slowing down,speedingup,slowing down,speedingup,Day 4: Applications; Gravity,s = position (height) s0= initial height v0= initial velocity t = time g= acceleration due to gravity g=9.8 m/s2 (meters and seconds) g=32 ft/s2 (fee

    17、t and seconds),s0,Day 4: Applications; Gravity,at time t= 0 an object at a height s0 above the Earths surface is given an upward or downward velocity of v0 and moves vertically (up or down) due to gravity. If the positive direction is up and the origin is the surface of the earth, then at any time t

    18、 the height s=s(t) of the object is :g= acceleration due to gravity g=9.8 m/s2 (meters and seconds) g=32 ft/s2 (feet and seconds),s axis,s0,Example,Nolan Ryan was capable of throwing a baseball at 150ft/s (more than 102 miles/hour). Could Nolan Ryan have hit the 208 ft ceiling of the Houston Astrodome if he were capable of giving the baseball an upward velocity of 100 ft/s from a height of 7 ft?,the maximum height occurs when velocity = 0,t=100/32=25/8 seconds,s(25/8)=163.25 feet,


    注意事项

    本文(Calculus.ppt)为本站会员(刘芸)主动上传,麦多课文档分享仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。 若此文所含内容侵犯了您的版权或隐私,请立即通知麦多课文档分享(点击联系客服),我们立即给予删除!




    关于我们 - 网站声明 - 网站地图 - 资源地图 - 友情链接 - 网站客服 - 联系我们

    copyright@ 2008-2019 麦多课文库(www.mydoc123.com)网站版权所有
    备案/许可证编号:苏ICP备17064731号-1 

    收起
    展开