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Newton's second law is insufficient to describe the motion of a particle. In addition, it requires a value for F, obtained by considering the particular physical entities with which the particle is interacting. For example, a typical resistive force may be modelled as a function of the velocity of the particle, for example:

[tex] \mathbf{F}_{\rm R} = - \lambda \mathbf{v}[/tex]

with λ a positive constant. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion. Continuing the example, assume that friction is the only force acting on the particle. Then the equation of motion is

[tex] - \lambda \mathbf{v} = m \mathbf{a} = m {d\mathbf{v} \over dt}.[/tex]

This can be integrated to obtain

[tex] \mathbf{v} = \mathbf{v}_0 e^{- \lambda t / m} [/tex]

can some body show me step by step the intergration there?

thanks!

(Edited by HallsofIvy to correct LaTex.)

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# Integration of newton equation?

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