Motion, Displacement, Velocity and Acceleration

Motion

Motion is a state in which an object changes its position with respect to time and its initial starting point.
If an object changes its position with respect to its surroundings in a given period of time then the object is said to be in motion.
Rest is the state of being stationary; the object does not change its position with time.

Displacement

Displacement is a vector quantity that describes an object’s overall change in position.
It is measured from the initial position to the final position, directly (the ‘shortest path’), not the path travelled.
It has both a magnitude (size) and direction.
It can be zero if the object returns to the start point, even after a long path was travelled.
It is usually represented with an arrow where the length of the arrow represents magnitude and the direction of the arrow signifies the direction of the displacement.

Velocity

Velocity is a vector quantity that represents the rate of change of an object’s displacement.
It includes both speed and direction.
Velocity = Displacement / Time Taken
Velocity can be constant, or it may change (increase or decrease) over time which implies that the object is accelerating.
Changes in velocity could occur due to changes in speed, direction, or both.

Acceleration

Acceleration is a vector quantity that measures how quickly velocity changes.
It includes both speed and direction.
Acceleration = Change in Velocity / Time Taken
Positive acceleration (or simply, acceleration) is when velocity is increasing over time, whereas negative acceleration (also called deceleration) is when velocity is decreasing over time.
An object can be accelerating even if its speed is constant, provided the direction of motion is changing.
Free-falling objects are under acceleration due to gravity, towards earth.

The Link Between These Concepts

These concepts are interrelated. Displacement incorporates a change in position, velocity includes a change in displacement, and acceleration involves changes in velocity.
Understanding these concepts is crucial to unravelling the specifics of how an object moves, changes position, and responds to forces that may exert influence.
Remember that direction is critical when dealing with vector quantities like displacement, velocity, and acceleration.