Question

derive the expression for this energy for an object moving with velocity V and having mass M

Answer 1

Work done = energy spent

( according to the work energy theorum)

Work done = f×s--------1

according to the newtons equations;

v^2=u^2 + 2as

taking a ( acceleration) as acceleration due to gravity;

v^2=u^2 + 2gs

taking s as the subject of equation ;

2gs= v^2-u^2

since initial velocity is 0

2gs= v^2

s= v^2/2g---------2

substituting s in equation 1;

work done = f× v^2/2g

f= ma
a=g
f= mg

therefore ;
the work done = mg× v^2/2g
= m × v^2/2
= 1/2m× v^2
therfore;
energy spent= 1/2mv^2