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
- Instantaneous velocity is the derivative of x with respect to time i.e
- Average acceleration is
- Instantaneous acceleration is the derivative of v with respect to time (in other words the second derivative of the position with respect to time)
In one dimension, the equations of motion assuming constant acceleration are as follows: