The slope of kinetic energy vs. displacement curve of a particle in motion is:

inversely proportional to acceleration of the particle.

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directly proportional to acceleration of the particle.

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equal to acceleration of particle.

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none of the above.

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Solution

The correct option is A directly proportional to acceleration of the particle.
$K E \propto v^{2} \frac{d}{d t} (K E) \propto 2 v \frac{d}{d t} v = 2 v a$
$\frac{d K}{d s} = \frac{d K}{d v} \frac{d v}{d s} = m v \frac{a}{v} \propto a$

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The slope of kinetic energy vs. displacement curve of a particle in motion is:

The correct option is A directly proportional to acceleration of the particle.KE∝v2ddt(KE)∝2vddtv=2vadKds=dKdvdvds=mvav∝a

The correct option is A directly proportional to acceleration of the particle.
$K E \propto v^{2} \frac{d}{d t} (K E) \propto 2 v \frac{d}{d t} v = 2 v a$
$\frac{d K}{d s} = \frac{d K}{d v} \frac{d v}{d s} = m v \frac{a}{v} \propto a$