# Acceleration

## Abstract

IN NATURE, NO. 1415, p. 125, Prof. Lodge asserts that the subject of acceleration is at the root of the perennial debate between engineers and teachers of mechanics; and he urges clearness of idea and accuracy of speech on all who deal with the junior student. Towards this end I would suggest that the too common phrase “acceleration of velocity” should be abandoned when the idea intended is “velocity of velocity.” V and V ought not to be confounded. Let the student be told that the time-rate of change of a particle's speed in any given fixed direction at a given instant is called the acceleration of the particle in the given direction at the given instant. If the direction of the particle's motion at the given instant makes an angle θ with the given fixed direction L, and if the speed of the particle in its own direction at this instant is V, its speed in the direction L is V cos θ. The time-rate of change of this is called the acceleration of the particle in the direction L. It is [!-- Equation --] units of speed per unit of time. If = θ = 0, L coincides with the line of motion, hence the acceleration of a particle along its line of motion is &Vdot; units of speed per unit of time. If [!-- Equation --]; coincides with a normal, hence the acceleration of the particle along a normal is, Vθ, i.e. it is the product of the linear speed and the angular speed. Linear speed is expressed in units of length per unit of time; angular speed is expressed in units of angle per unit of time. Acceleration is expressed in units of speed per unit of time.

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