Λparticle is moving in the x-y plane. Λt t=0, it is located at the origin O(0,0) and its velocit

step 1 At any time t, here I can write the expression as y is equal to UYT plus half aY t square. So, y

Λparticle is moving in the x-y plane. Λt t=0, it is located...

$\Lambda$ particle is moving in the $x-y$ plane. $\Lambda t t=0$, it is located at the origin $O(0,0)$ and its velocity is $\vec{v}-a(\sqrt{3} \hat{i}+\hat{j})$ where $a$ is a positive constant and $\hat{i}, \hat{j}$ are unit vectors in the positive $x$ and positive $y$ directions. Its acceleration is constant and given by $\vec{f}-(\hat{i} \mid \hat{j}) . \mathrm{In}$ its subsequent motion $(t>0)$ it will cross the $x$ -axis at the instant of time given by: (a) $t-a$ (b) $t-\sqrt{3} a$ (c) $t-2 a$ (d) $t-2 \sqrt{3} a$

$\Lambda$ particle is moving in the $x-y$ plane. $\Lambda t t=0$, it is located at the origin $O(0,0)$ and its velocity is $\vec{v}-a(\sqrt{3} \hat{i}+\hat{j})$ where $a$ is a positive constant and $\hat{i}, \hat{j}$ are unit vectors in the positive $x$ and
positive $y$ directions. Its acceleration is constant and given by $\vec{f}-(\hat{i} \mid \hat{j}) . \mathrm{In}$ its subsequent motion $(t>0)$ it will cross the $x$ -axis at the instant of time given by:
(a) $t-a$
(b) $t-\sqrt{3} a$
(c) $t-2 a$
(d) $t-2 \sqrt{3} a$

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Key Concepts

Trajectory Analysis

Trajectory analysis involves examining the path or curve that a moving particle follows under the influence of its initial velocity and constant acceleration. By understanding the motion components and applying kinematic equations, one can predict key events in the trajectory, such as the specific time at which the particle crosses an axis.

Constant Acceleration Kinematics

This concept involves analyzing the motion of a particle under a constant acceleration by using vector equations to determine how its position, velocity, and displacement evolve over time. It provides the foundational framework to solve problems in two-dimensional motion by considering the acceleration components independently along each coordinate axis.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its components along mutually perpendicular directions, typically the x and y axes. This approach is crucial in two-dimensional kinematics as it allows the independent analysis of movement in each direction, making it easier to determine when a particle crosses a particular axis by setting the corresponding coordinate to zero.

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