Newtonian mechanics

Newtonian mechanics

1. General equation of motion

   • For a body of mass \(m\) subjected to a net force of \(\mathbf{F}\) the acceleration, \( \mathbf{a} \) is given by: \[ \mathbf{a} = \frac{\mathbf{F}}{m} \]
   • In 1D
     • \[ a = \frac{F}{m} \]
     • Constant linear acceleration
       • Displacement equations
         • For a body with an initial velocity \(u\) subjected to a constant acceleration of \(a\) for a time \(t\), the displacement, \(s\), of the body from its initial location is governed by: \[s = ut + \frac{1}{2}at^2\]
       • Velocity equations
         • For a body with an initial velocity of \(u\), subject to a constant linear acceleration of magnitude \(a\) for a time \(t\), the final velocity of the body, \(v\), is governed by \[ v = u + at \].
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