Position Path Length Displacement

Introduction

If the position of any object changes relative to the time it is said to be in motion. The motion of any object happens in three ways like one-dimensional motion, two-dimensional motion, and three-dimensional motion. The movement of a train on a straight track, and the circular motion of the top are some examples of motion. This motion of particles is best described by the law of mechanics. Three laws were proposed for the understanding of the movement of an object. When there is a motion then there will be a displacement.

What is motion?

If the particle moves from one place to another, then it is in motion. Linear motion is the movement of particles from one place to another place with respect to time along a straight path called linear motion. So linear motion can also be defined as the change in displacement with respect to time. If the motion of the particle is along a straight line then it is said to be in linear motion. If the motion of the particle is in the circular path then it is said to be circular or orbital motion. It is also said to be angular motion. Pushing a box, and the motion of bullets from the gun are some examples of linear motion. Rotation of earth, disc throw, and motion of a stone tied by a rope are some examples of rotational or angular motion.

Explain position, path length

Position

The change in position denotes the motion. The rectangular coordinates system is used to define the coordinates of the position of the object. There are three axes which pass through a point called origin (O). They are x, y and z axes which are perpendicular to each other. Position of the object depends upon the motion of the object. For example the position of the object needs only one coordinate if it undergoes one dimension motion.

Similarly for three dimensional motion three coordinates are required. The position of the object along the x axis is calculated by taking the zero point as a reference. The position of the object which lies to the right of zero is taken as positive and the left is taken as negative.

Path length

The distance between the final initial and final position of the object denotes the path length. In the following figure let us consider the motion of the cycle from A to B. The path length of the cycle to cover the distance from A to B is 4m. Let us consider that the cycle moves from A to B then B to C and then from C to A. The total distance covered or the path length the cycle covered is 4 + 3 + 5 = 12m. If the object moves in a circular path then the total distance covered by the object is given by 2πr.

Displacement with examples

If the particle moves from one location to another location then the particle is said to be in motion. The distance traveled in a certain time following the direction of motion is called displacement. Thus the displacement is a vector quantity. An arrow mark is used to express the direction of displacement. As it is a vector quantity its direction is denoted with the help of arrow marks. Let us consider the movement of a ball from one place to another. Displacement is the difference between the final and initial position of the ball. Let the final and initial position of the moving ball be df and di. Then the displacement of the ball is

$$\mathrm{Displacement=d_f-d_i}$$

The unit of displacement is also meter(m). It is based on the S.I unit of the system. The dimensional formula for displacement is M⁰ L¹ T⁰. The examples for displacements are a teacher moving back and forth in front of the blackboard, and someone playing in a rectangular path.

What is the difference between the path length and distance?

• Distance is the length of the object that is travelled between any two points.

• The path length of the object is the distance travelled by the object between the two points. So the path length and the distance are the same. The S.I unit of both is m.

Difference between path length and displacement

Path length	Displacement
The total length of the path that the objects travels to reach the destination	The distance traveled in a certain time following the direction of motion is called displacement.
Scalar	Vector
It depends upon the path	It does not depends upon the path
The path length is always positive	The displacement may be zero or negative

Conclusion

If the object is changing its position then it is denoted as it is in motion. It may be in a linear motion or ic a circular motion. There are three numbers of coordinates that are required to describe the position of the object in the space. The change in the location of the object is known as displacement. The magnitude of the length between the initial and final position of the object is path length.

FAQs

1. Describe Newton’s first law of motion.

Newton’s first law implies that the particle does not change its state of motion or rest without applying an external force. For example, a box at a rest position is moved by a person by applying force to that box. Without giving force it cannot be moved. Similarly, the ball rolling cannot be stopped without applying a force to stop the motion.

2. Why is the displacement a vector quantity while distance is a scalar?

Distance is the measurement taken by considering only the magnitude of the length of the path whereas the displacement is a measurement in which both magnitude and direction are taken into consideration.

3. Can distance or displacement be negative?

Distance cannot be negative because it is a scalar quantity. But displacement can be negative as it shows the direction also. Thus the negative sign of displacement shows the direction.

4. What happens to the angular motion when the force is stopped suddenly?

If the object is moving in a circular path, it is mainly due to the centripetal force on it. That is why it is rotating in the same path. If the force is stopped then the object undergoes linear motion in the tangential direction.

5. Differentiate vector and scalar.

Scalar	Vector
Gives magnitude only	Gives both direction and magnitude
Used for only one-dimensional problem	It is used for multi-dimensional problem
It can be divided into another scalar	It cannot be divided into another vector quantity
Ex: distance, speed	Ex: displacement, velocity