As an object falls freely does kinetic energy of the object increase?

Answer 1

Kinetic energy increases. The kinetic energy is related to the velocity, KE=1/2mv2. As an object falls freely the velocity increases and therefore the kinetic energy increases. or this will be a good answer to go by when an object has more potential energy. It will transform into kinetic energy.

Answer 2

The object has also potential energy

due to the presence of the gravitational field of the earth

E_pot = F_g h

Here h is height above ground and F_g=g m is the gravitational force

(g ... gravitational accelation 9.81 m/s^2, m=mass of object).

What is constant is total energy, i.e. the sum of potential and kinetic energy

E_total = E_kinetic + E_pot.

Indeed as the object falls, it is accelarated as its time-dependent speed obeys

v(t) = g t

hence

E_kinetic(t)l = m v^2/2 = m g^2 t^2 / 2.

At the same time, the potential energy decreases as the height above ground is getting smaller

E_pot(t) = m g h(t)

with

h(t)=h(0) integral_0 t dt' v(t) =h(0) - g t^2/2.

Now

E_kinetic(t) + E_potential(t) = m g^2 t^2 /2 + g h(0) - m g^2 t^2 /2 = g h(0).