Question

A particle of mass $2 \mathrm{~kg}$ is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is (A) $10 \mathrm{~ms}^{-1}$ (B) $20 \mathrm{~ms}^{-1}$ (C) $75 \mathrm{~ms}^{-1}$ (D) $50 \mathrm{~ms}^{-1}$

Name: Problem 346, Chapter 3: JEE Physics
Uploaded: 2021-10-03T09:28:33-08:00
Duration: 2 min 50 s
Channel: Vysakh M
Description: A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is (A) 10 ms^-1 (B) 20 ms^-1 (C) 75 ms^-1 (D) 50 ms^-1

    A particle of mass $2 \mathrm{~kg}$ is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is
(A) $10 \mathrm{~ms}^{-1}$
(B) $20 \mathrm{~ms}^{-1}$
(C) $75 \mathrm{~ms}^{-1}$
(D) $50 \mathrm{~ms}^{-1}$

JEE Physics

StemEZ 1st Edition

Chapter 3, Problem 346

Instant Answer

Solved by Expert Vysakh M

10/03/2021

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The graph is divided into four sections, each representing a different force acting on the particle over a certain period of time. Show more…

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A particle of mass $2 \mathrm{~kg}$ is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is (A) $10 \mathrm{~ms}^{-1}$ (B) $20 \mathrm{~ms}^{-1}$ (C) $75 \mathrm{~ms}^{-1}$ (D) $50 \mathrm{~ms}^{-1}$

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Key Concepts

Impulse?Momentum Theorem

The impulse–momentum theorem states that the change in the momentum of an object is equal to the impulse applied to it. This principle allows one to calculate the final momentum, and subsequently the final velocity, of an object by relating the area under a force–time graph to the object's mass.

Newton’s Second Law

Newton’s second law establishes the proportionality between the net force acting on an object and its acceleration, with the mass of the object being the constant of proportionality. This law underpins the calculation of acceleration, which when integrated over time gives the velocity change experienced by the object.

Impulse

Impulse is the integral of force with respect to time and represents the total effect of a force acting over a time interval. It is computed as the area under a force–time graph and fundamentally quantifies how much momentum is transferred to an object during the interval.

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