Question

The slope of kinetic energy and displacement curve for a particle in motion will be

• A. Equal to the acceleration of the particle
• B. Directly proportional to the acceleration of the particle
• C. Inversely proportional to the acceleration of the particle
• D. None of the above

Answer 1

Answer: (B)

Directly proportional to the acceleration of the particle

Kinetic energy of a particle in motion $E=\frac{1}{2}m{v}^2$
Differentiating w.r.t. $x$, we get
$\frac{dE}{Dx}=\frac{1}{2}m\times 2v\frac{dv}{dx}$
$=mv\times \frac{dv}{dt}\times \frac{dt}{dx}$
$=mv\times \frac{a}{v}=ma$.
So, the slope of kinetic energy - displacement curve is directly proportional to the acceleration of the particle.