Position and velocity need an observer. The roadside origin stays at x = 0. The bus origin moves at the bus velocity, so its coordinates subtract the bus displacement. Both descriptions refer to the same walker at the same time.
Position states where the walker is relative to an origin. Displacement is final position minus starting position. Distance adds the lengths of all travelled parts. Reversing direction can cancel displacement while distance continues to increase.
The secant joining two positions gives average velocity over that interval. The tangent at the current time gives instantaneous velocity. Speed is the magnitude of instantaneous velocity, while average speed uses the full distance travelled. A varying acceleration makes the distinction between a secant and tangent visible.
Cart A covers equal displacements in equal time intervals because its velocity is constant. Cart B has a changing velocity when its acceleration is nonzero. Their position graphs can cross even when their slopes differ.
Acceleration is the rate of change of velocity. When velocity and acceleration have opposite signs, speed decreases until velocity reaches zero. Continued acceleration then starts motion in the opposite direction. The displacement equations use signed displacement.
Differentiating a position graph gives velocity; differentiating velocity gives acceleration. Integrating the signed velocity area gives displacement, while integrating acceleration gives the change in velocity. Initial position and initial velocity supply the constants needed to reconstruct the journey.
Relative position compares the car with the bus rather than with the road origin. Its rate of change is the car velocity minus the bus velocity. If this relative velocity is positive, the car closes an initial gap behind the bus. Changing the observer leaves their relative position unchanged.