### 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. ...

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