Paradox related to displacement and energy

[deleted-369089]

I have found this paradox and i can't find the solution.I need help

Malo's Bus Paradox
Consider an object 'x' moving from A to B and consider another object 'y' moving from A to B through 'C'(ABC is a triangle and AB is the diagonal) Let the displacements be s_x( I will be referring to subscripts with _ before the letter/number) and s_y, the time taken to coplete the journey be t_x and t_y, and let their masses be equal.And let t_y > t_x.Let the initial velocity be 0 and let both the objects be accelerated.
We know that the displacements are the same(AB) s_x = s_y = s
F=ma s=ut + 0.5at^2 (u is initial velocity and a is acceleration)
s=1/2 a t^2
2s/t^2 = a
F=2sm/t^2
Since displacement is the only vector here, the direction of force depends on the direction of displacement. Thus, the direction of force = direction of displacement cos(x) where x is the angle between the direction of force and displacement = 0 cos(0) = 1
We know W=F.s.cos(x) =2ms/t^2 . s
= 2m*s^2/t^2
We know the masses and displacements are equal for both objects Therefore the numerators are equal
W_y = 2ms^2/(t_y)^2
W_X = 2ms^2/(t_x)^2
We know t_y > t_x
1/t_y < 1/t_x
1/(t_y)^2 < 1/(t_x)^2
Therefore if we compare W_y & W_x
W_y < W_x or more energy required is for the object x than for object y.
But this goes against our intuition as we would say , by just looking, that energy for y must be greater than the energy required for x.
HOW IS THIS POSSIBLE!!!!
I need answers plz. Thank you

[deleted-2131]

Hi amalolan,

These forums are for students, parents, and teachers working on K-12 science projects. Your question sounds related to a HW problem or other assignment. In that case, you will get a more useful response if you post your question in a different set of online forums.

[deleted-369089]

Thanks a lot.I will do as you said and post this somewhere else and hope i get an answer. Thank you