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CAT Relative Speed: S1 – S2 - Practice Questions & MCQ

Edited By admin | Updated on Oct 05, 2023 05:01 PM | #CAT

Quick Facts

  • 5 Questions around this concept.

Solve by difficulty

The distance between two stations A and B is 440 km. A train starts at 4 p.m. from A and move towards B at an average speed of 40 km/hr. Another train starts B at 5 p.m. and moves towards A at an average speed of 60 km/hr. How far from A will the two trains meet and at what time?

A father starts from home at 3 :00 p.m. to pick his son from school One day the school got over early, at 3:00 p.m. The son start walking home. He met his father on the way and both returned 15 minutes early then the usual time. If speed of father is 35kmph then find speed of son in kmph?


Concepts Covered - 1

Relative Speed: S1 – S2


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


\mathrm{S_{\text {relative }}=\left|S_1-S_2\right| }


- \mathrm{S_1}  is the speed of the first object

\mathrm{S_2}  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?


Given speeds:

\mathrm{S_1}  = 50 km/h

\mathrm{S_2}  = 70 km/h

Relative speed:

\mathrm{S_{\text {relative }}=\left|S_2-S_1\right|=|70-50|=20 \mathrm{~km} / \mathrm{h}}

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.


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