In mathematics, the comparison between motions of two objects or comparison among multiple objects’ motion is said to be relative motion. Equations have been made to describe the motions of the objects depending on the place in which motions are taking place. In this study, the concept of relative motion will be explained. In addition, the relative motion formula will be stated throughout this study. Furthermore, the relative motion examples will be illustrated by the end of this study.

Discussion

What is Relative Motion?

Relative motion can be defined as the mathematical difference between the motion of two or among more objects. This implies that relative motion is used in mathematics to calculate the motion of a particular object with respect to other moving objects. Therefore, it is not calculated in reference to the motion of the earth. Instead, it is calculated based on the reference of some other moving objects. Wherever an object moves around its surface the position of the object continuously alters. These changes in the positions of the object are generally calculated in reference to a point. However, based on the location in which the motion of an object taking place can be of different dimensions. On the other hand, the motion of an object takes place in space then it is said to be three dimensions. Therefore, one, two, and three functions can be used to specifically determine the position of a particular object at any time. The significance of relative motion is that it is a useful approach to solve problems related to physics, to design robotic devices, automatic pilots, or some other video games. 

Relative Motion Formula 

Assume that, the motion of an object X in comparison with another object Y is ‘v’. 

Then, the motion of object Y in comparison with object X will be ‘v’.

Condition one:

Suppose two objects that are moving in a similar direction must have one object with the highest speed and another object with a lower speed. In such a situation, relative motion can be calculated as shown below:

Relative motion = velocity of object X (Greater speed) – velocity of object Y (Minor speed)

Condition two:

Suppose an object (first object) is moving around another object (second object) and the second object is being stationary. In such a situation, the relative motion can be calculated as shown below:

Relative motion = velocity of the first object (moving object) – velocity of the second object (static object – zero) 

Condition three:

Suppose two objects, object X and object Y are moving in the opposite direction. In such a situation, the relative motion can be calculated as:

Relative motion = velocity of Object X + velocity of object Y

Relative Motion Examples in Mathematics 

Assuming that a man (first person) is traveling in a car and the car is moving at 200 kilometers per hour speed. Therefore, the speed of the man (first person) in reference to another man (second person) sitting beside him in the car is zero. According to the second person, the first person is not moving. However, a woman (third person) who stands on the ground observes the first person outside from the car. According to the third person, the first person is moving at 200 kilometers per hour speed because the first person is inside the car, and the car is moving at a 200 kilometers per hour speed.

Relative Motion Example 1:

If two bodies P and Q are traveling in opposite directions at the same speed 150 km/h, then what will be the relative speed of P with respect to Q? 

Given, 

Speed of P and Q = 150 km/h, traveling in opposite directions. 

Concept used,

Relative motion = velocity of Object P + velocity of object Q

Solution,

The relative speed of P with respect to Q = 150 + 150 = 300 km/h. 

Conclusion 

After the discussion, it can be concluded that the relative motion delivers significant importance in various fields of mathematics, physics, and engineering. It is a beneficial approach to calculate the speed of one body in reference to some other moving bodies at a time. Additionally, if the time and speed of two or more objects are mentioned in a situation then it will help to calculate the distance as well. In this study, different conditions and relative motion examples are discussed that will help to understand the application of relative motion immensely.