PHYSICS 8A-02 (01-21-10) (1) - PHYSICS 8A Professor Joel...

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PHYSICS 8A Professor Joel Fajans 1/21/10 Lecture 2 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS Please drop this course if you do not intend to take this class, so people can get off the waitlist. This class has an early drop deadline. The last day to drop this course is next Friday. LECTURE Today I will continue our discussion of 1D kinematics. This should mostly be a review for those of you who have taken physics before. Last time, we discussed relations between distance and velocity. We came up with a few relations: ݔൌݒݐ This formula is good for constant velocity. Another relation we came up with is ݒൌ ݀ݔ ݀ݐ Note on this graph we have an initial x , so to the first equation we add ݔ : ݔൌݔ ൅ݒݐ Now we discuss objects which have constant acceleration. t x 20ݐ 1 20 20 2 80 80 3 180 180 4 320 320 Recall that at the end of last lecture we discussed how to determine the position given the velocity and time travelled: ݒ ݔ ݐ ݔ ݒ ݐ ݔ ݔ ݒ ݐ ݐ ݐ ݒ ݒ ݒ
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PHYSICS 8A ASUC Lecture Notes Online: Approved by the UC Board of Regents 1/21/10 D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. 2 I claim that I can generalize this method to find the position of an object to the case where velocity is not constant. ݔൌ 1 2 ݐݒ ݔൌ 1 2 ܽݐ Another way of doing this is by integration: ݔൌ න ݒሺݐሻ݀ݐ ൌ න ܽݐ݀ݐ ݔൌ 1 2 ܽݐ ൅ݔ Yet another way of doing this is by guessing what sort of displacement would make this all work out. In other words, say that: ݔൌܺሺݐሻ Where x is the position and X is a function which gives the position. What can we say about X ? We know that velocity is always the derivative of this unknown function with respect to time. That is, ݒൌ ݀ܺ ݀ݐ I use the identity equating
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PHYSICS 8A-02 (01-21-10) (1) - PHYSICS 8A Professor Joel...

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