The complexity of an equation is majorly determined by the number of parameters that vary in it. It becomes obvious that linear motion is easy to understand and predict.
Then you should wonder why we’re discussing it. Just as a thing becomes simple, its usage multiplies. If you would restrict the motion of a body to only be allowed in one direction, this forms the basis for a linear motion to occur.
Now let us discuss the various appliances where this can apply varying in difficulty and accuracy. You all have used a Vernier caliper once in your life.
By controlling the linear motion, you can achieve a very degree of accuracy. Similarly, you can understand the concept that goes into building parts that have relative linear motion among them. Parts that slides over or into each other.
Consider the example of hydraulic suspensions. The fluid is entrapped on one arm and the other arms move side the one with a fluid in it. Depending upon the velocity with which these parts are allowed to move concerning our design, we can achieve a certain level of damping of transmission of force.
According to Maxwell, a rotating body loses energy and thus in case of a linear motion when compared under similar conditions, it looses much less energy. Though the concept of linear motion can be relative, depending upon the frame of reference taken. A car that Is moving in a single direction might appear to be in a linear motion to you but if a fish that is inside a spherical bowl was to observe this car, it would appear to be moving on a circular path.
The best example of linear motion is undoubtedly the linear motion of light. Light executes linear motion and this forms the basis for optical mechanics which is a whole different field of study.