Question 133: Motion in 2D & Vectors

Question

A particle is moving with velocity $$\overrightarrow v  = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a constant. The general equation for its path is

Accepted Answer

$$\overrightarrow v  = k\left( {y\widehat i + x\widehat j} \right)$$  ........(1)
Also $$\overrightarrow v = {v_x}\widehat i + {v_y}\widehat j$$
$$\overrightarrow v = {{dx} \over {dt}}\widehat i + {{dy} \over {dt}}\widehat j$$ ........(2)
Equating (1) and (2), we get
$${{dx} \over {dt}} = ky\,\,\,\,\,\,$$ .......(3)
and $$\,\,\,\,\,{{dy} \over {dt}} = kx$$ ......(4)
Dividing (3) and (4), we get
$${{dy} \over {dx}} = {x \over y} $$
$$\Rightarrow ydy = xdx$$
Integrating both sides of above equation, we get
$$\int {ydy}  = \int {xdx} $$
$$ \Rightarrow {y^2} = {x^2} + $$ constant

Answer

y = x2 + constant

Answer

y2 = x + constant

Answer

xy = constant

Answer

y2 = x2 + constant

Motion in 2D & Vectors

A particle is moving with velocity $\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$, where K is a constant. The general equation for its path is

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