A body with mass 5 kg is acted upon by a force 𝐅=(-3 𝐢̂+4 ĵ) N. If its initial velocity at t=0

step 1 In this question we have given a body whose mass is 5kG and it is acted by a force. We have give

A body with mass 5 kg is acted upon by a force 𝐅=(-3 𝐢̂+4...

A body with mass $5 \mathrm{~kg}$ is acted upon by a force $\mathbf{F}=(-3 \hat{\mathbf{i}}+4 \hat{j}) \mathrm{N}$. If its initial velocity at $t=0$ is $\mathbf{v}=(6 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}) \mathrm{ms}^{-1}$, the time at which it will just have a velocity along the $y$-axis is (a) never (b) $10 \mathrm{~s}$ (c) $2 \mathrm{~s}$ (d) $15 \mathrm{~s}$

A body with mass $5 \mathrm{~kg}$ is acted upon by a force $\mathbf{F}=(-3 \hat{\mathbf{i}}+4 \hat{j}) \mathrm{N}$. If its initial velocity at $t=0$ is $\mathbf{v}=(6 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}) \mathrm{ms}^{-1}$, the time at which it will just have
a velocity along the $y$-axis is
(a) never
(b) $10 \mathrm{~s}$
(c) $2 \mathrm{~s}$
(d) $15 \mathrm{~s}$

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Key Concepts

Newton's Second Law

Newton's Second Law establishes that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass (F = ma). This fundamental principle allows one to compute the acceleration of a body when the applied force and the mass are known, and is a cornerstone in dynamics.

Vector Decomposition

Vector decomposition involves breaking a vector into its orthogonal (independent) components, such as the horizontal and vertical directions. This method is essential when analyzing problems where forces and velocities act in multiple directions, allowing each dimension of motion to be handled separately.

Constant Acceleration Kinematics

Constant acceleration kinematics deals with the motion of bodies under uniform acceleration. It provides equations that relate displacement, initial velocity, acceleration, and time. This concept is used to determine various motion parameters when acceleration does not change over time, thereby simplifying the analysis of linear motion in each direction.

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