A particle of mass 2 kg moves with an initial velocity of v=(4 î+4 ĵ) m / s. A constant force o

step 1 In this question we have given a particle of mass 2 kg and it moves with an initial velocity whi

A particle of mass 2 kg moves with an initial velocity of...

A particle of mass $2 \mathrm{~kg}$ moves with an initial velocity of $v=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$. A constant force of $F=-20 \hat{j} \mathrm{~N}$ is applied on the particle. Initially, the particle was at (0, 0). The $x$ -coordinate of the particle when its $y$ -coordinate again becomes zero is given by a. $1.2 \mathrm{~m}$ b. $4.8 \mathrm{~m}$ c. $6.0 \mathrm{~m}$ d. $3.2 \mathrm{~m}$

A particle of mass $2 \mathrm{~kg}$ moves with an initial velocity of $v=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$. A constant force of $F=-20 \hat{j} \mathrm{~N}$ is
applied on the particle. Initially, the particle was at (0,
0). The $x$ -coordinate of the particle when its $y$ -coordinate again becomes zero is given by
a. $1.2 \mathrm{~m}$
b. $4.8 \mathrm{~m}$
c. $6.0 \mathrm{~m}$
d. $3.2 \mathrm{~m}$

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Key Concepts

Newton's Second Law

This fundamental principle of mechanics states that the net force acting on an object equals its mass multiplied by its acceleration (F = m.a). It is used to determine how a constant force affects the acceleration of a particle, providing the link between the force applied and the resulting motion in each component direction.

Kinematic Equations for Constant Acceleration

These equations describe the motion of objects under constant acceleration. They enable calculation of displacement, velocity, and time in each independent direction by relating initial velocity, acceleration, and time. For instance, in one dimension, the equation s = ut + 1/2at² is often used to find the displacement when time and acceleration are known.

Projectile Motion Analysis

Projectile motion involves objects moving under the influence of gravity (or any constant vertical acceleration) while having independent horizontal motion. In this analysis, the horizontal component of motion remains constant due to zero horizontal force, while the vertical component undergoes constant acceleration. This allows separate treatment of x and y motions, where the time of flight determined from vertical motion is then used to compute the horizontal displacement.

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