What is Motion, Reference Point, Distance and Displacement?

Motion is the change of position of an object from one point to other in a given period of time. Motion can be described using different entities such as some of the following:

  • Reference point: In order to define the position of an object, one needs to understand the concept of the reference point and a set of axes. 
    • For three dimensional coordinate system comprising of mutually perpendicular x, y and z-axis, the intersection point of these axes are called as a reference point. It is also called the origin. 
    • For a two-dimensional coordinate system having x and y-axis as mutually perpendicular axes, the point of intersection becomes the reference point, also termed as the origin.
    • For a one-dimensional system, the point where the motion starts can be taken as the reference point also termed as the origin.
  • The frame of reference: Frame of reference comprises a reference point (origin) and is used to describe the motion of the body with respect to time.
  • Distance: Distance traveled by a body is the length of the path traveled of the body in a given frame of reference. Let's say in one-dimensional (x-axis) frame of reference, the position of a body moving in a straight line is 10 meter at time t1 and 25 meters at t2 and 15 meters in the backward direction at t3. Therefore, the distance traveled by the body is 10 + 25 + 15 = 50 meter.
  • Displacement: Displacement of the body is the final position of the body from the reference point. In other words, the shortest path from the reference point (origin) to the position of the body is the displacement of the body. Mathematically speaking, the displacement of a body having position x1 at time t1 and x2 at time 2 can be represented as the following:

    \[x_2 - x_1\]

    Thus, if the position of the body at time t1 is 10 meters and time t2 is 5 meters from the reference point (origin) in x-axis (one-dimension), the displacement can be calculated as the following:

    5 - 10 = -5 meters

    It must be noted that in above example, the displacement is negative. It can be inferred that the displacement of a body can be either positive or negative. The displacement has both magnitude and direction. This is the property of a vector entity.

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