Rectilinear Motion

If the coordinate system is oriented such that the x-axis coincides with the line of motion, the general equations for position, displacement, velocity, and acceleration simplify to

Position
Displacement
Velocity
Acceleration
Third Derivative of Position?

Velocity acts in the same direction as displacement.
Accelerations acts colinearly with velocity.

If v and a have the same sign, then v is increasing (particle is accelerating).
If v and a have opposite signs, then v is decreasing (particle is decelerating).

Distance traveled (a scalar) is a measure of the total length of a particle's path.
Displacment (a vector) is a measure of the difference between the beginning and the end of a particle's part.