Here, we have to find out the correct statement about the slope of the kinetic energy - displacement of a particle in motion According to work - energy theorem, Kinetic energy, E = Work done Also, work done = Force × displacement ie, W = FS Or, E = FS Also we know that, Force, F = mass × acceleration Therefore, E = maS ---- (1) Slope of E - S curve is
dE
dS
differentiating (1) with respect S
dE
dS
= ma Therefore, slope = ma Where, m is constant ∴ Slope α a That is, the slope of the kinetic energy - displacement of a particle in motion is directly proportional to the acceleration.