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# Relative Motion Notes I UPSC CSAT

Relative Motion is the motion of an object with respect to some other object. It is the velocity of one object as observed from the reference frame of another object. The relative velocity can be both positive and negative depending on the relative direction.

### Relative Motion in the Same Direction

If two objects are moving in the same direction, the relative velocity is the difference of their individual velocities:

$V_{\text{rel}} = V_A – V_B$

### Relative Motion in the Opposite Direction

If two objects are moving in opposite directions, the relative velocity is the sum of their individual velocities:

$V_{\text{rel}} = V_A + V_B$

## Application in Quantitative Aptitude:

Relative motion is often used to solve problems related to time, distance, and speed. Consider the scenario of two objects moving towards or away from each other.

### Example Problem:

Suppose two cars, A and B, are moving towards each other with speeds of 40 km/h and 60 km/h, respectively. What is their relative velocity, and how long will it take for them to meet if they start 120 km apart?

### Solution:

Calculate relative velocity:
$V_{\text{rel}} = V_A + V_B = 40 \, \text{km/h} + 60 \, \text{km/h} = 100 \, \text{km/h}$

$\text{Time} = \frac{120 \, \text{km}}{100 \, \text{km/h}} = 1.2 \, \text{hours}$

Understanding relative motion is crucial for solving quantitative aptitude problems involving moving objects and is applicable in various real-world scenarios, such as traffic analysis, pursuit problems, and more.