Q. The slope of the 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
Explanation
(c) $E = \frac{1}{2}mv^{2}$. Differentiating $w.r.t.$ $x$, we get
$\frac{dE}{dx} = \frac{1}{2}m \times 2v\frac{dv}{dx} = mv \times \frac{dv}{dt} \times \frac{dt}{dx} = mv \times \frac{a}{v} = ma$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.