Question

Derive the formula of kinetic energy step by step
{class 9 }

Answer 1

consider an object with mass m , moving with initial velocity u. let a force F , act on it causing a displacement s, along the direction of force and acceleration . Let the object attain final velocity v.

we known that F=m x a

1.by position velocity relation we have, V^2=U^2+2as or s=v^2-u^2

2.The work done by the force W=F x s

3.substituting 1 and 2 in 3
W=(m x a)x(v^2-u^2/2a)
W=m/2(v^2-u^2)
W=1/2mv^2-1/2mu^2

4.for an object to be at rest in the begging, u=0
Therefore, W=1/2mv^2

Workdone =kinetic energy

Therefore

→KE=1/2mv^2




I hope it will help u

Answer 2

Your answer ...

Let an object of mass= m , moving with a initial velocity = u , and the displacement is = s , and with the final velocity = v

We know that
W = F × s

F=ma---------(1.)

v2-u2=2as
s=v2-u2/2a---------(2.)

Put eq.(1.)= nd (2.)

W= m×a * v2-u2/2a
=m/2*(v2-u2)/2a
=1/2mv2-1/2u2

if initial velocity = 0

K.E = 1/2 mv²