A body of mass 5 kg starts from the origin with an initial...

A body of mass $5 \mathrm{~kg}$ starts from the origin with an initial velocity $\vec{u}=\left(30 \hat{i}+40^{\circ}\right) \mathrm{m} \mathrm{s}^{-1}$, If a constant force $(-6 \hat{i}-5 \hat{j}) \mathrm{N}$ acts on the body, the time in which the $y$-component of the velocity becomes zero is (a) $5 \%$ (b) 205 (c) $40 \mathrm{~s}$ (d) $80 \mathrm{~s}$

A body of mass $5 \mathrm{~kg}$ starts from the origin with an initial velocity $\vec{u}=\left(30 \hat{i}+40^{\circ}\right) \mathrm{m} \mathrm{s}^{-1}$, If a constant force $(-6 \hat{i}-5 \hat{j}) \mathrm{N}$ acts on the body, the time in which the $y$-component of the velocity becomes
zero is
(a) $5 \%$
(b) 205
(c) $40 \mathrm{~s}$
(d) $80 \mathrm{~s}$

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Key Concepts

Newton's Second Law

Newton's second law establishes the relationship between force, mass, and acceleration, stating that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle allows us to determine the acceleration resulting from any applied force given the mass, a critical step in solving many dynamics problems.

Vector Decomposition

Many physical quantities, such as velocity and force, are vectors and can be decomposed into components along mutually perpendicular directions (usually x and y axes). This decomposition facilitates the analysis of motion in each direction independently, especially when forces are acting in different directions.

Kinematics Under Constant Acceleration

When an object is subjected to a constant acceleration, its velocity changes linearly with time according to the kinematic equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time elapsed. This equation is particularly useful for finding the time at which a specific component of the velocity reaches a certain value, such as zero.

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