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6.3: Uniformly Accelerated Motion

If the only force on a body is a resistive force that is proportional to its speed, the equation of motion is

\[ m\ddot{x}= -b\dot{x}. \]

One thinks, for example, of Stokes's equation for the laminar motion of a sphere through a viscous fluid, in which the resistive force is \( 6\pi\eta a\upsilon\), where \( \eta\) is the coefficient of dynamic viscosity. If we divide both sides of the equation by the mass \( m\), we obtain

\[ m\ddot{x}= -\gamma\dot{x}, \]

where \( \gamma = \frac{b}{m}\) is the damping constant. It has dimension T-1 and SI units s-1.