A particle projected from origin moves in x-y plane with a velocity v- - 3- - 6 x- where - and - are the unit vectors along x and y axis- Find the equation of path followed by the particle-

The correct option is A y = x^2 We have, #160; v =3î +6xĵ #160; ⇒ dx / dt =3 ⇒ x=3t #160; Now, dy / dt =6x =18 ...

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Standard XII

Physics

Vectors and Its Types

A particle pr...

Question

A particle projected from origin moves in x-y plane with a velocity $\to v = 3^i + 6 x^j$ , where $^i$ and $^j$ are the unit vectors along x and y axis. Find the equation of path followed by the particle.

y = x^{2}

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y = \frac{1}{x^{2}}

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y = 2 x^{2}

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y = \frac{1}{x}

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Solution

The correct option is A $y = x^{2}$
We have,
$\begin{matrix} \to v = 3^i + 6 x^j \Rightarrow \frac{d x}{d t} = 3 \Rightarrow x = 3 t \end{matrix}$
Now,
$\begin{matrix} \frac{d y}{d t} = 6 x = 18 t \Rightarrow y = 9 t^{2} \Rightarrow y = x^{2} \end{matrix}$
Hence,
Option $A$ is correct answer.

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A particle projected from origin moves in x-y plane with a velocity →v=3^i+6x^j, where ^i and ^j are the unit vectors along x and y axis. Find the equation of path followed by the particle.

The correct option is A y=x2We have, →v=3^i+6x^j⇒dxdt=3⇒x=3tNow,dydt=6x=18t⇒y=9t2⇒y=x2Hence,Option A is correct answer.

A particle projected from origin moves in x-y plane with a velocity $\to v = 3^i + 6 x^j$ , where $^i$ and $^j$ are the unit vectors along x and y axis. Find the equation of path followed by the particle.

The correct option is A $y = x^{2}$
We have,
$\begin{matrix} \to v = 3^i + 6 x^j \Rightarrow \frac{d x}{d t} = 3 \Rightarrow x = 3 t \end{matrix}$
Now,
$\begin{matrix} \frac{d y}{d t} = 6 x = 18 t \Rightarrow y = 9 t^{2} \Rightarrow y = x^{2} \end{matrix}$
Hence,
Option $A$ is correct answer.