Question

1) Derive the formula kinetic energy =1/2 mv^2 and potential energy= mgh​

Answer 1

Answer:

For kinetic energy:-

1/2mv²

let an object of mass m is at rest. therefore, its initial velocity u= 0. when an external force f is applied on it, its velocity changes into v in t seconds and object covers a distance s.

Now,

we know that,

work done = Force×distance

or, { work done is also called as kinetic energy}

kinetic energy= ma× s

kinetic energy= mas

kinetic energy= m× v²/2 ........{v²= u²+2as}

kinetic energy= 1/2mv².

for potential energy:-

mgh

let a body of mass m is raised to height h against the force of gravity.

we know that,

Potential energy= work done to lift the object

potential energy= W

potential energy= force×distance

potential energy= mg× h......{ f= mg}

potential energy= mgh ..

hope it will help you