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)$$y=ut+\frac{1}{2}at^2$$ $$\frac{\text{d}y}{\text{d}t}=u+at$$
$$y''=a$$
