Advanced Engineering Mathematics, 7th Edition

9.2 Motion on a Curve

INTRODUCTION

In the preceding section we saw that the first and second derivatives of the vector function r(t) = 〈f(t), g(t), h(t)〉 = f(t)i + g(t)j + h(t)k can be obtained by differentiating the component functions f, g, and h. In this section we give a physical interpretation to the vectors r′(t) and r″(t).

Velocity and Acceleration

Suppose a particle or body moves along a curve C so that its position at time t is given by the vector function r(t) = f(t)i + g(t)j + h(t)k. If the component functions f, g, and h have second derivatives, then the vectors

are called the velocity and acceleration of the particle, respectively. ...