Slope of kinetic energy displacement curve of a particle in motion is

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5.Work, Energy, Power and Collision

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

A

Equal to the acceleration of the particle

B

Inversely proportional to the acceleration

C

Directly proportional to the acceleration

D

None of the above

Solution

(c) $E = \frac{1}{2}m{v^2}.$ Differentiating w.r.t. $x$, we get

$\frac{{dE}}{{dx}} = \frac{1}{2}m \times 2v\frac{{dv}}{{dx}} = mv \times \frac{{dv}}{{dt}} \times \frac{{dt}}{{dx}} = mv \times \frac{a}{v} = ma$

Standard 11

Physics

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