Newton�s first law is fundamental to our work in mechanics by v7166R


									Newton’s law is fundamental to our work in mechanics. Newton’s law relates the applied
force, F(t), to the resulting acceleration, a(t), by

                                   F(t) = m a(t)                                         (1)

Here the mass, m, is assumed to be constant and t is the time. Equation (1) is differential
equation that predicts where the mass m will be at any time if F(t) is a known, specified
function and the appropriate initial conditions are given. To realize this, the acceleration
may be written as the second derivative of time, or
                                    a(t)  2                                              (2)
where d denotes the total derivative and x denotes the displacement. Substitution of
Equation (2) into Equation (1) yields:
                                    d 2 x(t)
                                              F(t)                                       (3)
                                      dt 2
Equation (3) shows explicitly that Newton’s law results in a second order differential

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