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Standard XII

Physics

3rd Equation of Motion

A particle lo...

Question

A particle located at $x = 0$ at time $t = 0,$ starts moving along thepositive $x$ -direction with a velocity $v$ that varies as $v = a \sqrt{x}$ . Thedisplacement of the particle varies with time as:

t^{3}

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t^{2}

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t

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t^{1 / 2}

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Solution

The correct option is B $t^{2}$
$\begin{matrix} V = a \sqrt{x} \Rightarrow \int_{0}^{x} \frac{d x}{\sqrt{x}} = a \int_{0}^{t} d t = 2 \sqrt{x} = a t \Rightarrow x = \frac{a^{2}}{4} t^{2} A n s . (B) \end{matrix}$

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A particle located at x=0 at time t=0, starts moving along thepositive x -direction with a velocity v that varies as v=a√x . Thedisplacement of the particle varies with time as:

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The correct option is B $t^{2}$
$\begin{matrix} V = a \sqrt{x} \Rightarrow \int_{0}^{x} \frac{d x}{\sqrt{x}} = a \int_{0}^{t} d t = 2 \sqrt{x} = a t \Rightarrow x = \frac{a^{2}}{4} t^{2} A n s . (B) \end{matrix}$