I E Irodov Physical Fundamentals Of Mechanics (Relativistic Mechanics) Q. 1.378 Solution

I E Irodov Physical Fundamentals of Mechanics is one of the most recommended books of Physics for students preparing for JEE Advanced, Physics Olympiads and other competitive exams.

The chapter on Relativistic Mechanics deals with more complex topics, such as relativistic momentum, relativistic energy, force at high velocities and motion approaching the speed of light.

In this page you will find a full step-by-step solution to I E Irodov Physical Fundamentals of Mechanics (Relativistic Mechanics) Question 1.378 with the concepts and formulae used to solve the problem.

I E Irodov Relativistic Mechanics Question 1.378

Question:

A particle of rest mass mâ‚€ starts moving at time t = 0 under the action of a constant force F.

Find the time dependence of:

• The particle’s velocity v(t)
• The distance covered x(t)

Concepts Used in I E Irodov Q. 1.378

This problem is based on relativistic dynamics.

Important concepts include:

• Relativistic momentum
• Newton’s Second Law
• Constant force
• Lorentz factor
• Relativistic velocity
• Integration in relativistic motion

In traditional mechanics , a constant force leads to constant acceleration . This is not the case when velocities approach the speed of light . As the particle moves faster and faster , its momentum increases dramatically .

Easy Solution of I E Irodov Relativistic Mechanics Q. 1.378

Let:

• mâ‚€ = rest mass of the particle
• F = constant external force
• v = velocity of the particle
• c = speed of light
• t = time

Initially,

At t = 0

The particle starts from rest.

Therefore,

v = 0

Step 1: Write the Relativistic Momentum

Relativistic momentum is

[
p=\gamma m_0v
]

where

[
\gamma=\frac1{\sqrt{1-\frac{v^2}{c^2}}}
]

Since force is constant,

[
F=\frac{dp}{dt}
]

Step 2: Integrate the Momentum Equation

Since F is constant,

[
dp=Fdt
]

Integrating,

[
p=Ft
]

because initial momentum is zero.

Now,

[
\gamma m_0v=Ft
]

Step 3: Find the Velocity

Substitute

[
\gamma=\frac1{\sqrt{1-\frac{v^2}{c^2}}}
]

Therefore,

[
\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}=Ft
]

Squaring both sides,

F^2t^2
]

After simplification,

[
v=
\frac{Ftc}
{\sqrt{m_0^2c^2+F^2t^2}}
]

This is the required velocity-time relation.

Step 4: Find the Distance Covered

We know

[
v=\frac{dx}{dt}
]

Substitute the expression for velocity,

[
dx=
\frac{Ftc}
{\sqrt{m_0^2c^2+F^2t^2}}dt
]

Integrating,

m_0c
\right]
]

This is the required distance-time relation.

Final Answer

Velocity

[
\boxed{
v(t)=
\frac{Ftc}
{\sqrt{m_0^2c^2+F^2t^2}}
}
]

Distance Covered

m_0c
\right)
}
]

Simple Explanation of the Answer

In traditional mechanics, a constant force gives a constant acceleration.

But according to special relativity the particle can never go faster than light .

The particle is initially accelerating rapidly.

The same force is still being applied , but the increase in velocity slows down as the speed approaches c .

The momentum continues to grow, but the velocity approaches the speed of light asymptotically.

And this is why the velocity equation can never be equal to c.

Download Free JEE E-Book for Physics Preparation

Plan JEE Advanced Physics preparation with concepts, previous year questions, mock tests and selected advanced reference problems.

Download JEE E-BookExplore JEE Courses

Key Takeaways

Common Mistakes Students Should Avoid

Students commonly make the following mistakes:

• Using classical momentum (p=mv)
• Assuming acceleration remains constant
• Ignoring the Lorentz factor
• Forgetting that velocity can never exceed the speed of light
• Incorrect integration while finding displacement
• Mixing classical and relativistic formulas

Always begin with the relativistic momentum equation before applying Newton’s Second Law.

Why Practice I E Irodov Problems for JEE Advanced?

I E Irodov develops deep conceptual understanding beyond routine numerical problems.

Benefits include:

• Better analytical thinking
• Strong Physics concepts
• Improved mathematical application
• Confidence in difficult JEE Advanced problems
• Better preparation for Physics Olympiads

Students should solve selected I E Irodov questions after completing standard JEE Advanced problems.

Is I E Irodov Q. 1.378 a JEE Main Question?

Nope. I E Irodov Relativistic Mechanics Q. 1.378 This is not a JEE Main level problem.

This question is about advanced topics in relativistic dynamics when a constant force acts on a particle moving at speeds close to the speed of light. Better for advanced Physics preparation as it requires knowledge of relativistic momentum, Lorentz factor and integration techniques.

This question is recommended for:

• JEE Advanced aspirants
• Physics Olympiad students
• Students interested in advanced mechanics
• Learners who have completed the standard JEE Physics syllabus

For JEE Main, students should primarily focus on NCERT concepts, standard JEE-level numerical problems, previous year papers and mock tests.

Is Relativistic Mechanics Important for JEE?

Relativistic Mechanics is not a high weightage chapter for JEE Main. But it is useful for strengthening advanced Physics concepts required for JEE Advanced.

The chapter helps students to know:

• Special Theory of Relativity
• Relativistic Momentum
• Relativistic Energy
• Force at High Speeds
• Time Dilation
• Length Contraction
• Mass-Energy Relationship

Students should study this chapter after completing core Mechanics and Modern Physics topics.

Important Topics in I E Irodov Physical Fundamentals of Mechanics

How Should Students Use I E Irodov for JEE Advanced?

The best way to study I E Irodov is step by step.

Recommended preparation strategy:

Students should avoid attempting all I E Irodov questions at the beginning of their preparation. Instead, use the book as an advanced practice resource after developing strong fundamentals.

I E Irodov for NRI JEE Students

Selected I E Irodov questions are very useful for NRI students from USA, UAE, Saudi Arabia, Qatar, Oman, Kuwait and Bahrain preparing for JEE Advanced.

Students appearing for AP, IB, British or other international boards should first bridge the gap between their school syllabus and JEE syllabus before solving the advanced reference books.

A recommended preparation sequence is:

• Complete the JEE Physics syllabus
• Solve chapter-wise JEE questions
• Practice JEE Main and JEE Advanced previous year papers
• Attempt selected I E Irodov problems
• Regularly revise concepts and formulas

This approach helps students build strong conceptual understanding without becoming overwhelmed.

Related I E Irodov Relativistic Mechanics Questions

After completing Question 1.378, students can also practice:

• I E Irodov Relativistic Mechanics Q. 1.345
• I E Irodov Relativistic Mechanics Q. 1.350
• I E Irodov Relativistic Mechanics Q. 1.359
• I E Irodov Relativistic Mechanics Q. 1.388

Link each question to its corresponding TestPrepKart solution page to help students continue their preparation.

Practice Next

After solving this question, students should continue with:

• Relativistic Mechanics numerical problems
• JEE Advanced Physics previous year papers
• Mechanics revision notes
• Conservation of Momentum problems
• Modern Physics practice questions
• JEE Advanced mock tests

Regular practice of advanced questions improves analytical thinking and problem-solving speed.

Useful JEE, DASA & CIWG Resources for I E Irodov Physics

FAQs on I E Irodov Relativistic Mechanics Q. 1.378

1. What is the main concept used in I E Irodov Q. 1.378?

The problem is based on relativistic momentum and the motion of a particle under a constant force.

2. Is I E Irodov Q. 1.378 useful for JEE Main?

This question is above the usual JEE Main level and is mainly recommended for JEE Advanced preparation.

3. Why does the particle not exceed the speed of light?

According to Einstein’s theory of special relativity, the Lorentz factor increases rapidly as velocity approaches the speed of light. As a result, the particle’s speed approaches c but never reaches or exceeds it.

4. Which formula is most important in this question?

The most important relation is the relativistic momentum equation:

[
p=\gamma m_0v
]

where

[
\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
]

5. Is this question suitable for beginners?

No. Students should first complete basic Mechanics, Modern Physics and JEE-level questions before attempting this problem.

6. Is I E Irodov useful for JEE Advanced?

Yes. Selected I E Irodov problems help students develop advanced Physics concepts and improve their ability to solve challenging JEE Advanced questions.