Itachi, perhaps your calculations should be corrected as follows:
>*(From the 1st equation)*$$y=ut-uk+\frac{1}{2}at^2+\frac{1}{2}ak^2-atk$$
>$$\frac{\text{d}y}{\text{d}t}=u+at-ak$$

>$$y''=a$$

>*(From the 2nd equation)*$$y=ut+\frac{1}{2}at^2$$
>$$\frac{\text{d}y}{\text{d}t}=u+at$$

>$$y''=a$$