Mechanics: Chapter 1 – Motion in One Dimension

Motion in one dimension is fairly simple. I’ll break it down to you as briefly as possible. In one dimension, we essentially have one co-ordinate of position. Let’s call that x. Now velocity is the rate of change of x. Acceleration is the rate of change of the the velocity of x.

  • Average velocity is v = \frac{\Delta x}{\Delta t}
  • Instantaneous velocity is the derivative of x with respect to time i.e v = \frac{dx}{dt} = \dot{x}
  • Average acceleration is a = \frac{\Delta v}{\Delta t}
  • Instantaneous acceleration is the derivative of v with respect to time (in other words the second derivative of the position with respect to time) a = \frac{dv}{dt} = \dot{v} = \ddot{x}

In one dimension, the equations of motion assuming constant acceleration are as follows:

  • v = v_{0} + at
  • x = x_{0} + ut + \frac{1}{2}at^2
  • x = x_{0} + \frac{1}{2}(v_{0}+v)t
  • v^2 = v_{0}^2 + 2as
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