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Physics · MOTION IN A STRAIGHT LINE
हिन्दीThe velocity of a particle moving along a straight line varies with position \( x \) as \( v = k \sqrt{x} \), where \( k \) is a positive constant. What is the acceleration of the particle?
Correct answer · Option 4
\( \frac{k^2}{2} \)
Explanation
Acceleration using calculus is \( a = v \frac{dv}{dx} \). Here \( \frac{dv}{dx} = \frac{k}{2\sqrt{x}} \). Thus \( a = (k\sqrt{x}) \cdot (\frac{k}{2\sqrt{x}}) = \frac{k^2}{2} \).
