The position of a point in time $\text{'}t\text{'}$ is given by $x=a+bt-c{t}^2,y=at+b{t}^2$, Its acceleration at time $\text{'}t\text{'}$ is:

Acceleration m $x$- direction $=\frac{d^{2}x}{d{t}^2}=-2c$

an acceleration in $y$- direction $=\frac{d^{2}y}{d{t}^2}=2b$

Resultant acceleration is $=\sqrt{(-2c{)}^2+(2b{)}^2}=2\sqrt{b^2+c^2}$