Your Federal Quarterly Tax Payments are due April 15th Get Help Now >>

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

VIEWS: 0 PAGES: 1

									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
                                             d2x
                                    a(t)  2                                              (2)
                                             dt
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
equation.

								
To top