Kinetic energy K and displacement x are related as K=F.x (work-energy theorem) So, slope of K−x curve is
dK
dx
=
d
dx
Fx=F( let force is constant) ∴ Slope of K−x curve = Force= Mass × Acceleration or
dK
dx
∝a (statement I is correct) Statement II is incorrect because ball rises again to same height as it was dropped, therefore it is the case of perfectly elastic collision and hence, no loss of energy occurs. Also, for a body starting from rest, KE = Work done ⇒
1
2
mv2=Fx=m⋅a⋅x ⇒v=√2ax which is mass independent. ∴ Statement III is incorrect.