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

Options

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

B

Explanation

(b) Kinetic energy of a particle in motion `E=(1)/(2)mv^(2)`
Differentiating w.r.t.x, we get
`(dE)/(dx)=(1)/(2)mxx2v(dv)/(dx)`
`=mvxx(dv)/(dt)xx(dt)/(dx)=mvxx(a)/(v)=mv`
So, the slope of kinetic energy-displacement curve is directly proportinal to the acceleration of the particle.