Page:Elementary Text-book of Physics (Anthony, 1897).djvu/30

The practical unit of velocity is the velocity of a point moving, uniformly through one centimetre in one second.

The dimensions of velocity are $LT^{-1}$.

Velocity, which is fully defined when its magnitude and direction are given, is a vector quantity, and may be represented by a straight line. Velocities may therefore be compounded and resolved by the rules already given for the composition and resolution of vectors.

17. Acceleration.— When the velocity of a point varies, either by a change in its magnitude, or by a change in its direction, or by changes in both, the rate of change is called the acceleration of the point. Acceleration is either positive or negative, according as the velocity increases or diminishes. If the path of the point be a straight line, and if equal changes in velocity occur in equal times, its acceleration is constant. It is measured by the ratio of the change in velocity to the time during which that change occurs. If $v_{0}$ and $v$ represent the velocities of the point at the instants t^ and t, then its acceleration is represented by

$a={\frac {v-v_{0}}{t-t_{0}}}\cdot$

(4)

Fig. 8If the path of the point be curved, or if the changes in velocity in equal times be not equal, the acceleration is variable. A variable acceleration in a curved path may always be resolved into two components, one of which is tangent and the other normal to the path. We will consider the case in which the path lies in a plane. Let $A$ and $B$ (Fig. 8) be two points in the path very near each other, from which normals are drawn on the concave side of the curve, meeting at the point $O$, and making with each other the angle $\alpha$. In the limit, as $\alpha$ vanishes, the lines $OA$ and $OB$ become equal and are radii of curvature of the path at the