x and y co-ordinates of a particle moving in x-y plane at some instant are x=2 t^2 and y=(3 / 2)

step 1 Hello students our question is x and y coordinate of a particle moving in x y plane as some inst

X and y co-ordinates of a particle moving in x-y plane at...

$x$ and y co-ordinates of a particle moving in $\mathrm{x}-\mathrm{y}$ plane at some instant are $\mathrm{x}=2 \mathrm{t}^{2}$ and $\mathrm{y}=(3 / 2) \mathrm{t}^{2}$ Calculate y co-ordinate when its $\mathrm{x}$ coordinate is $8 \mathrm{~m}$. (A) $3 \mathrm{~m}$ (B) $6 \mathrm{~m}$ (C) $8 \mathrm{~m}$ (D) $9 \mathrm{~m}$

$x$ and y co-ordinates of a particle moving in $\mathrm{x}-\mathrm{y}$ plane at some instant are $\mathrm{x}=2 \mathrm{t}^{2}$ and $\mathrm{y}=(3 / 2) \mathrm{t}^{2}$ Calculate y co-ordinate when its $\mathrm{x}$ coordinate is $8 \mathrm{~m}$.
(A) $3 \mathrm{~m}$
(B) $6 \mathrm{~m}$
(C) $8 \mathrm{~m}$
(D) $9 \mathrm{~m}$

Key Concepts

Parametric Equations

Parametric equations express the coordinates of the points on a curve as functions of a variable, often time. This representation is widely used in mathematics and physics to describe the trajectory or motion of a particle, where each coordinate (such as x and y) depends on a common parameter, enabling a more flexible description of motion compared to explicit functions.

Elimination of the Parameter

Elimination of the parameter is a method used to remove the independent parameter from a set of parametric equations to establish a direct relationship between the variables. This technique simplifies the problem by allowing one to substitute the parameter’s value, obtained from one equation, into the other, making it easier to compute specific coordinates or analyze the geometry of the path.

Particle Motion in Two Dimensions

Describing particle motion in two dimensions involves using separate parametric equations for each coordinate, typically with time as the common parameter. This approach enables the examination of how the particle moves along different axes, and it is essential in understanding trajectories, determining positions at given instances, and analyzing the dynamics of the motion.

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