Velocity and Acceleration

Velocity and Acceleration - ME 210 Applied Mathematics for...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Velocity and Acceleration along a Curve If a body (represented by a point P) moves along a path C whose parametric representation is given by its position vector, then the successive derivatives and of can be attributed to two kinematic concepts, namely the velocity and the acceleration , respectively. The vector defined by t ) t ( r ) t t ( r lim t ) t ( r dt ) t ( r d ) t ( r ) t ( v 0 t 0 t is tangent to the curve C and, therefore, points in the instantaneous direction of motion of P. ) t ( r ) t ( r ) t ( r
Background image of page 1

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

View Full DocumentRight Arrow Icon
ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 We also know from the Equation that this vector has a magnitude dt ds ) t ( r ) t ( r dt ) t ( r d ) t ( r ) t ( v where s is the arc length, which measures the distance of P from a fixed point (s = 0) on C along the curve C. Hence, ds/dt is the speed of P, and the vector is, therefore, called as the velocity or the velocity vector of the motion of P along C. Since the velocity vector is defined only and only for those points belonging to the curve C along which P moves, it constitutes a vector field . Similarly, the speed ds/dt is also defined only and only for those points belonging to the curve C along which P moves; but since it is a scalar quantity, in turn, it constitutes a scalar field . Both speed and velocity fields have a common domain of definition: The curve C along which P moves.
Background image of page 2
ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Another way of representing the relationship between the velocity (a vectorial
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/31/2011 for the course ME 210 taught by Professor Farukarinç during the Spring '09 term at Middle East Technical University.

Page1 / 14

Velocity and Acceleration - ME 210 Applied Mathematics for...

This preview shows document pages 1 - 4. Sign up to view the full document.

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