alittlebitofcalculus-pdf-january2011-111112001007-phpapp01

543210987654321 2109876543210987654321

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 182 We need to be more clear about the terms CHANGE in position, displacement , displacement and distance travelled in A) 1-Dimension in fixed direction , B) fixed axis distance fixed fixed or 1-Dimension with CHANGE in direction and C) 2-Dimensions. These terms need to be explained from both the Calculus point of view and the Physics (what is happening in nature) point of view and how they are related. A) 1-Dimension in fixed direction : in the example the car travelled East in a fixed fixed direction, that is to say moving along a straight line without reversing or changing direction. So in this very speical case from the Physics point of view: Physics CHANGE in position = displacement = distance travelled . displacement distance Also, from the Calculus point of view, over a given interval, say [t 1 , t 2 ] : CHANGE in position = t2 ∫ t1 x’(t)dt = area under the speed cur ve area curv ar This is because the SPEED function did NOT CHANGE SIGN. In 1-Dimensional motion the SPEED function will CHANGE SIGN only if there is a CHANGE in direction. B) fixed axis or 1-Dimension with CHANGE in direction : Let us review an example fixed of the projected ball. 1-Dimension y(t1) y(T/ 2) y’(t1) y(t2) 0987654321 0987654321 0987654321 0987654321 0987654321 0987654321 0987654321 0987654321 1 0987654321 098765432654321 654321 654321 654321 654321 654321 654321 T/ 2 (0,0) t2 t1 y’(t2) T t vertical speed y ’(t) = u . s i n θ -- g t 183 CHANGE in position over [t1, t2] = dispalcement = y (t2) -- y(t1) distance travelled =| ∫ T /2 t1 t2 ∫ t1 y ’(t)dt = y(t2) -- y(t1) y ’(t)dt| + | ∫ t2 T/ 2 y ’(t)dt| = |y(T/ 2 )| -- y(t1) | + | y(t2) -- y(T/ 2)| The distance travelled (odometer reading or length of path) in the usual (nondistance mathematical) sense is used to convey the notion “CHANGE in position” But position”. in Calculus these two are different. “CHANGE in position” is always with reference to a co-ordinate system. If an object moves in a circle o...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern