Case Study:

Riya was traveling in a train moving at a speed of 90 km/h. To fully grasp her journey, it helps to first master the basics of distance and displacement in everyday travel. While looking out of the window, she noticed another train on a parallel track moving in the same direction. Surprisingly, despite both trains moving at high speeds, the other train appeared almost stationary for a few seconds. However, when the other train started moving in the opposite direction, it appeared to pass by very quickly.

To investigate this observation, Riya noted that the second train was moving at 85 km/h in the same direction initially. Later, when moving in the opposite direction, its speed remained the same. She found it confusing that the same train could appear slow at one moment and extremely fast at another.

This situation highlights the concept of relative motion. Since motion is rarely just about speed, understanding the crucial differences between speed and velocity is key to solving why the train's direction changed Riya's perception.

where the observed motion of an object depends on the motion of the observer. The difference or sum of velocities determines how fast or slow an object appears to move when viewed from another moving frame of reference.

Before diving into the questions, you can visualize these motion patterns through simple graphs to see how speed changes over time.

CASE-BASED QUESTIONS

MCQ

Q1. When both trains move in the same direction, the apparent speed of the second train is:
A. 175 km/h
B. 5 km/h
C. 90 km/h
D. 85 km/h

Q2. When the trains move in opposite directions, the apparent speed becomes:
A. 5 km/h
B. 90 km/h
C. 175 km/h
D. 0 km/h

Assertion - Reason

Q3. Assertion (A): The second train appears almost stationary when both trains move in the same direction.
Reason (R): The relative velocity between the two trains is very small.

A. Both A and R are true, and R is the correct explanation
B. Both A and R are true, but R is not the correct explanation
C. A is true, R is false
D. A is false, R is true

Application-Based

Q4. If Riya’s train increases speed to 100 km/h while the other remains at 85 km/h in the same direction, how will the apparent motion change?

Q5. Why does the second train appear to move faster when traveling in the opposite direction even though its actual speed remains unchanged?

Data/Logic-Based

Q6. Calculate the relative velocity of the second train with respect to Riya when:
a) Both trains move in the same direction
b) Both trains move in opposite directions

ANSWER KEY WITH EXPLANATION

A1. B (5 km/h)
Explanation: Relative velocity = 90 - 85 = 5 km/h. Small difference makes it appear slow.

A2. C - (175 km/h)
Explanation: Relative velocity = 90 + 85 = 175 km/h when moving opposite.

A3. A - Explanation: Both statements are correct. Small relative velocity causes near stationary appearance.

A4. Explanation: Relative speed becomes 100 - 85 = 15 km/h, so the second train appears faster than before.

A5. Explanation: Relative velocity increases due to addition of speeds in opposite direction, making motion appear faster.

A6. a) 5 km/h (90 - 85)
b) 175 km/h (90 + 85)
Explanation: Relative velocity depends on direction of motion (NCERT principle).

Ready to take your calculations further? Learn how to apply the three equations of motion to solve even more complex physics problems.

Master Your Physics Exams: Practice makes perfect! Strengthen your Class 9 preparation by downloading our Physics Worksheets. If you're feeling confident, try these unsolved practice papers or check your progress with our solved sample papers.

HOTS EXTENSION QUESTIONS

Q1. If two trains have equal speeds and move in the same direction, what will a passenger observe? Justify mathematically and conceptually.

Q2. Can an object appear at rest even when both observer and object are moving? Explain with a real-life example other than trains.

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