Answer:
It is worth noting that the higher the gravitational energy of an object moving downwards, the lower the kinetic energy, and the lower the kinetic energy of an object moving upwards, the higher its gravitational energy.
Gravitational potential energy is acquired by an object when it has been moved against a gravitational field. For example, an object raised above the surface of the Earth will gain energy, which is released if the object is allowed to fall back to the ground.
Nothing happens to velocity at all. Speed and direction remain constant.
Newton's second law states that the product between the mass and the acceleration of an object is equal to the force applied:

from which we find an expression for the acceleration:

(1)
Both objects are moving by uniformly accelerated motion (because the force applied is constant), so we can also using the following relationship

(2)
where

is the final speed of the object

is the initial speed
S is the distance covered
By substituting (1) into (2), and by removing

(since the final velocity of the two objects is zero), we find


where we can ignore the negative sign (because the force F will bring another negative sign).
For the first object, we have
![S= \frac{(2.0 m/s)^2 (4.0 kg)}{2F} = \frac{8}{F} [m]](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7B%282.0%20m%2Fs%29%5E2%20%284.0%20kg%29%7D%7B2F%7D%20%3D%20%20%5Cfrac%7B8%7D%7BF%7D%20%5Bm%5D%20)
And for the second object we have
![S= \frac{(4.0 m/s)^2 (1.0 kg)}{2F} = \frac{8}{F} [m]](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7B%284.0%20m%2Fs%29%5E2%20%281.0%20kg%29%7D%7B2F%7D%20%3D%20%5Cfrac%7B8%7D%7BF%7D%20%5Bm%5D%20)
And since the braking force applied to the two objects is the same, the two objects cover the same distance.
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