Question

A particle of mass $2 \mathrm{~kg}$ starts moving in a straight line with an initial velocity of $2 \mathrm{~ms}^{-1}$ at a constant acceleration of $2 \mathrm{~ms}^{-2}$. Then rate of change of kinetic energy (a) is four times the velocity at any moment (b) is two times the displacement at any moment (c) is four times the rate of change of velocity at any moment (d) is constant through out

Name: Problem 18, Chapter 7: Master Resource Book in JEE Main Physics
Uploaded: 2022-02-10T17:54:15-08:00
Duration: 1 min 55 s
Channel: Subash Charan
Description: A particle of mass 2 kg starts moving in a straight line with an initial velocity of 2 ms^-1 at a constant acceleration of 2 ms^-2. Then rate of change of kinetic energy (a) is four times the velocity at any moment (b) is two times the displacement at any moment (c) is four times the rate of change of velocity at any moment (d) is constant through out

   A particle of mass $2 \mathrm{~kg}$ starts moving in a straight line with an initial velocity of $2 \mathrm{~ms}^{-1}$ at a constant acceleration of $2 \mathrm{~ms}^{-2}$. Then rate of change of kinetic energy
(a) is four times the velocity at any moment
(b) is two times the displacement at any moment
(c) is four times the rate of change of velocity at any moment
(d) is constant through out

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 7, Problem 18

Instant Answer

Solved by Expert Subash Charan

02/10/2022

Step 1

Step 1: The rate of change of kinetic energy is given by the formula $\frac{dK}{dt} = m \cdot a \cdot v$, where $m$ is the mass of the particle, $a$ is the acceleration, and $v$ is the velocity. Show more…

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A particle of mass $2 \mathrm{~kg}$ starts moving in a straight line with an initial velocity of $2 \mathrm{~ms}^{-1}$ at a constant acceleration of $2 \mathrm{~ms}^{-2}$. Then rate of change of kinetic energy (a) is four times the velocity at any moment (b) is two times the displacement at any moment (c) is four times the rate of change of velocity at any moment (d) is constant through out

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Key Concepts

Kinetic Energy

Kinetic energy represents the energy that an object possesses due to its motion, calculated using the formula KE = (1/2) m v^2. It is a core concept in mechanics that links the mass and velocity of an object to its capacity to perform work as it moves.

Rate of Change of Kinetic Energy (Power)

The rate of change of kinetic energy with respect to time, often referred to as power, is computed using the derivative of the kinetic energy expression, resulting in d(KE)/dt = m v (dv/dt). This equation illustrates how changes in an object's velocity (acceleration) directly affect the dynamics of its energy.

Constant Acceleration

Constant acceleration implies that the rate of change of velocity remains uniform over time. This assumption simplifies analyses within kinematics and dynamics, allowing for clear relationships to be drawn between acceleration, velocity, and the derivative of kinetic energy.

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