I.E. Irodov Problem No. 1.97 is an important problem from the Physical Fundamentals of Mechanics section of Problems in General Physics. It deals with a particle initially at rest that is acted upon by a time-dependent force. The problem asks us to determine the momentum acquired by the particle after the force stops acting and the distance travelled while the force is acting. This problem is particularly useful for students preparing for JEE Advanced Physics, because it demonstrates how Newton's second law can be combined with integration to solve a non-uniform force problem. In this article, we will discuss the I.E. Irodov Problem 1.97 Solution step by step and understand the important concepts involved. I.E. Irodov Problem 1.97 – Problem Concept At t=0, a stationary particle of mass m is acted upon by a time-dependent force F = a t(τ−t) where a is a constant vector and τ is the total time for which the force acts. The force becomes zero at t=τ. The problem asks us to find: The momentum of the particle when the force stops acting. The distance travelled by the particle during the action of the force. This makes Irodov Problem 1.97 an excellent application of the impulse-momentum theorem and Newton's second law. Part (a): Momentum of the Particle We know that force is related to momentum by F = dt d p ​ ​ Therefore, d p ​ = F dt Initially, the particle is stationary, so p ​ 0 ​ =0 At t=τ, the momentum is therefore p ​ =∫ 0 τ ​ F dt Substituting the given force, p ​ =∫ 0 τ ​ a t(τ−t)dt Taking the constant vector a outside, p ​ = a ∫ 0 τ ​ (τt−t 2 )dt Integrating, p ​ = a [ 2 τt 2 ​ − 3 t 3 ​ ] 0 τ ​ Putting t=τ, p ​ = a ( 2 τ 3 ​ − 3 τ 3 ​ ) Hence, p ​ = 6 a τ 3 ​ ​ Thus, the momentum acquired by the particle when the force ceases to act is p= 6 aτ 3 ​ ​ in the direction of a . This result illustrates the important principle that the change in momentum is equal to the impulse of the force.

These results follow directly from integrating the time-dependent force. Why Irodov Problem 1.97 Is Important for JEE Advanced The Irodov Problem 1.97 Solution is valuable because it teaches students how to handle a force that changes continuously with time. In many competitive-examination problems, force is not constant, and simply using F=ma with a single numerical value is not sufficient. The key ideas demonstrated here are: Time-dependent force Newton's second law Momentum and impulse Integration of force with respect to time Velocity as a function of time Integration of velocity to obtain displacement Dimensional understanding of physical quantities Students preparing for JEE Advanced Physics should practice such problems carefully because they develop the mathematical and conceptual skills required for advanced mechanics. Learn Irodov Problems with Shivendra Sir If you are looking for detailed Irodov Problems with Solutions, this problem is a good example of how a seemingly complicated mechanics question can be solved systematically. The best approach is to first identify the physical quantity being asked for, write the appropriate fundamental equation, substitute the time-dependent force, and then integrate using the correct limits. For more physics learning resources and detailed problem-solving sessions, visit physicshometutor.com. By Shivendra Sir Contact: 9811767503 Conclusion I.E. Irodov Problem No. 1.97 provides an excellent application of Newton's laws and calculus in mechanics. The central idea is that a time-dependent force must be integrated to determine the momentum, while velocity must subsequently be integrated to determine the distance travelled. For students preparing for JEE Main, JEE Advanced, Olympiads, and other competitive examinations, mastering these techniques can significantly improve their ability to solve advanced Law of Motion and mechanics