rev_rect_motion

rev_rect_motion - J. Peraire Dynamics 16.07 Fall 2004...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: J. Peraire Dynamics 16.07 Fall 2004 Version 1.1 REVIEW - Rectilinear Motion We start by considering the simple motion of a particle along a straight line. The position of particle A at any instant can be specified by the coordinate s with origin at some fixed point O . The instantaneous velocity is ds v = dt = ˙ v . (1) We will be using the “dot” notation, to indicate time derivative, e.g. (˙) ≡ d/dt . Here, a positive v means that the particle is moving in the direction of increasing s , whereas a negative v , indicates that the particle is moving in the opposite direction. The acceleration is dv d 2 s ¨ a = = v ˙ = = s . (2) dt dt 2 The above expression allows us to calculate the speed and the acceleration if s and/or v are given as a function of t , i.e. s ( t ) and v ( t ). In most cases however, we will know the acceleration and then, the velocity and the position will have to be determined from the above expressions by integration. Determining the velocity from the acceleration From a ( t ) If the acceleration is given as a function of t , a ( t ), then the velocity can be determined by simple integration of equation (2), t v ( t ) = v 0 + a ( t ) dt . (3) t 0 Here, v 0 is the velocity at time t , which is determined by the initial conditions. From a ( v ) If the acceleration is given as a function of velocity a ( v ), then, we can still use equation (2), but in this case we will solve for the time as a function of velocity, v dv t ( v ) = t 0 + . (4) a ( v ) v 0 1 Once the relationship t ( v ) has been obtained, we can, in principle, solve for the velocity to obtain v ( t ). )....
View Full Document

This note was uploaded on 01/12/2012 for the course ENG 102 taught by Professor Eke during the Winter '08 term at UC Davis.

Page1 / 4

rev_rect_motion - J. Peraire Dynamics 16.07 Fall 2004...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online