Since the graph between $y$ and $t$ is a parabola.

$y=t^2, v_x=\frac{dx}{dt}=1$ and $a_x=\frac{d{v}_x}{dt}=0$ and $v_y=\frac{dy}{dt}=2t$ and $a_y=2m{s}^{-2}$

The force acting on the particle is 

$F=m{a}_y=\left(0.5kg\right)\left(2m{s}^{-2}\right)=1N$ along $y$ axis