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Continuous motion has a defined way of moving in terms of position, velocity and acceleration, whereas, erratic motion has changing motion whereby its position, velocity and acceleration are hard to describe using one continuous mathematical equation in the path. This motion would have to be dissected and studied by segments.
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Click for notes on Rectilinear kinematics: Erratic motion
Continuous motion is the primary course in Physics, however, in Dynamics, students would much more understand how the basic equations applied to this subject have been derived through Calculus. Furthermore, examples would be applying differentiation and integration - more advanced functions from Physics.
Erratic motion deals more on graphs to help visualize the motion of the body. The s-t, v-t, and a-t graphs are used to identify the parameters for this kind of motion. And with the rich variance of how graphs would appear, erratic motion computation would usually be imploring segments which are later added together to arrive at a certain answer.
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