i would like to get the solution of this quesiton

(i) Given that,
where

Differentiating both sides….
(
As , so
(ii) Given that;
As per law of conservation of energy;
Dividing and removing mass m in both sides, we get
Substituting v from above equation and
Rearranging above equation proves that;
(iii) Given conditions are
(iv) In...