Relative Speed for CLAT - Practice Questions & MCQ

Explanation:

When two objects are moving in the same direction, their relative speed with respect to each other is the difference of their speeds.

Mathematically:

Where:

-   is the speed of the first object

-   is the speed of the second object

The absolute value ensures that the relative speed is always non-negative.

Foundation Building Questions :

Question: Two cars start from the same point. The first car is moving at 50 km/h and the second car is moving at 70 km/h. What is the relative speed of the second car with respect to the first?

Solution:

Given speeds:

-   = 50 km/h

-   = 70 km/h

Relative speed:

Answer: The relative speed of the second car with respect to the first car is 20 km/h.

Tips and Tricks:

1. Visualising the Problem: Draw a number line or use arrows to represent the direction. This will help ensure you're subtracting the speeds in the right order, especially when objects move in opposite directions.

2. Conversion of Units: Always ensure that the speeds of both objects are in the same units. If one speed is given in m/s and another in km/h, use the conversion techniques from Concept 5.

3. Application of Previous Concepts: Relative speed plays an essential role in problems where time and distance calculations are needed. Be ready to apply the fundamental equation  S = DT after finding the relative speed.

4. Interplay with Other Movements: Relative speed is especially crucial when understanding problems with trains passing each other or when objects overtake each other. Recognizing the type of movement helps in deciding whether to add or subtract the speeds.

Relative speed forms the foundation of many complex problems in the Time, Speed, and Distance domain. Understanding the core principles and practising a variety of problems will ensure students are well-prepared to tackle questions in entrance exams. Always remember to read the problem statement carefully to determine the nature of movement (same direction, opposite direction, etc.) and apply the correct relative speed calculation.

Explanation:

When two objects are moving towards each other, i.e., in opposite directions, their relative speed with respect to each other is the sum of their speeds.

Mathematically:

Where:

-  is the speed of the first object

-  is the speed of the second object

Foundation Building Questions :

Question: Two trains are heading towards each other on parallel tracks. The first train is moving at 60 km/h, and the second train is moving at 40 km/h. What is their relative speed?

Solution:

Given speeds:

- = 60  km/h

- = 40  km/h

Relative speed:

Answer: The relative speed of the two trains with respect to each other is 100 km/h.

Tips and Tricks:

1. Direction is Key: Always ascertain the direction of movement of the two objects. If they are moving towards each other (opposite directions), their relative speed is the sum of their speeds.

2. Unit Consistency: Make sure both speeds are in the same unit. Use the conversion techniques from Concept 5 if necessary.

3. Applying Previous Concepts: Once you determine the relative speed, you can use it in conjunction with the fundamental equation S = DT  to solve for time or distance, depending on the problem.

4. Visualisation: Drawing a quick sketch with arrows representing the direction of movement can be quite beneficial, especially in problems with multiple moving objects.

5. Incorporate Other Concepts: Remember the formula for relative speed when two objects move in the same direction from Concept 6. It's common for exams to have mixed problems, where understanding both concepts becomes vital.

Understanding the nature of the movement and correctly determining the relative speed are critical steps in solving many problems in the Time, Speed, and Distance chapter. Practise different types of problems, ensuring you can quickly and accurately determine the direction of movement and apply the correct relative speed formula.