Question

state work energy theorem prove it for variable force​

Answer 1

Answer:

Work energy theorem -

It states that the work done by the net force acting on a body is equal to the changed produced in kinetic energy of the body. 

Let F be the variable force 

∴ Work done by this variable force , W=∫xixfF⋅dx

where xi is the initial position 

and xf is final position.

Also Kinetic energy of an object , K=21mv2 

⟹dtdK=mvdtdv

⟹dtdK=madtdx

⟹dtdKFdtdx

⟹dK=Fdx

⟹∫KiKfdK=∫xixfF⋅dx

⟹ΔK=W

Where ΔK is the change in kinetic energy 

Answer 2

ANSWER

Work energy theorem

lit states that the works done by the net force acting on a body is equal to the changed produced in kinetic energy of the body.

EXPLANATION

we use equation of motion v square - v square =2as

multiplying both sides by m/2 we get

mv square /2 + mv square of motion by Newton second law

F = ma

now

mv square /2 - mv square /2 = FS = w

then it can be written aas

kf - ki

I HOPE IT WILL HELP YOU