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
differentiating (1) with respect S
= 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.