Question

hi derive the formula of kinetic energy

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

Amount of work done is called energy.

Work = energy.

Energy = Fs ____________ (1)

Consider a body of mass m is initially at rest after time t is start moving with Final velocity v due to uniform acceleration a and cover the distance s.

From Newton' s 2nd law of motion,

F = ma


From 3rd eqⁿ of motion,

v² - u² = 2as

If u = 0

v² = 2as

s = v² / 2a

Putting the value of F and s in eqⁿ 1

K.E. = Fs

= ma × v² / 2a

= m × v² / 2

= 1/2 mv²


K. E. = 1/2 mv²


HOPE IT HELPS YOU..

Answer 2

Consider a body of mass ' m ' , which I at rest . Let the constant force ' F ' act on it and displaces it through a distance ' S ' in time ' t '

Let ' v ' be the velocity of the body at the end of the time ' t ' .

The acceleration produced I the body a = change in velocity / time interval

a = v - u/t. ... ( since u = 0 )

a = v/t

therefore force acting on the body is given by

F = ma

= m × v/t

the displacement of the body is given by

s = average velocity × time

s = v + u/2 × t

= v + 0 / 2 × t

= vt/2

so s = vt/2

work done by the force is given by

W = FS

= mv/t × vt/2

= mv^2/2

Kinetic energy can be expressed as the amount of work done by the body before coming to rest

so

Kinetic energy = 1/2 mv^2