A particle is in motion on the x-axis. The variation of its velocity with position is as shown. The

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A particle is in motion on the x-axis. The variation of its velocity with position is as shown. The graph is circle and its equation is x² + v² =1, where x is in m and v in m/s. The CORRECT statement(s) is/are

Accepted Answer

Sol. x2 + v2 = 1⇒ $2x + 2v\frac{dv}{dx} = 0$⇒ $v\frac{dv}{dx} = - \overrightarrow{x} = \overrightarrow{a}$⇒ $Q\left( \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$ ⇒ xQ = $\frac{1}{\sqrt{2}} \Rightarrow |a| = \frac{1}{\sqrt{2}}$

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