Linear motion

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Linear motion is motion in one dimension, usually on a line.

An example of linear motion is throwing a ball straight up and having it come back straight down. In linear motion there is only an x value to represent displacement and x varies with t (time).

The velocity of a particle in one dimensional linear motion may be found by differentiating with respect to t. The acceleration may be found by differentiating the velocity. The converse is also true, to find the velocity when given the acceleration simply integrate. To find displacement simply integrate the velocity.

This can be demonstrated graphically. The gradient of a line on the displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under an acceleration time graph gives the velocity.