A First Approach to Classical Mechanics

Abstract

We begin by considering the motion of a single particle in ${\mathbb{R}}^{1},$ which may be thought of as a particle sliding along a wire, or a particle with motion that just happens to lie in a line. We let x(t) denote the particle’s position as a function of time. The particle’s velocity is then

$$\displaystyle{v(t) :=\dot{ x}(t),}$$

where we use a dot over a symbol to denote the derivative of that quantity with respect to the time t.