A Very Fast Start

Given that acceleration $a = t^2 \text{ m/s}^2$ , then velocity

$\begin{aligned} v(t) & = \int a(t) \ dt = \int t^2 \ dt = \frac {t^3}3 + C_1 & \small \blue{\text{where }C_1 \text{ is the constant of integration.}} \\ v(0) & = C_1 = 10 \\ \implies v(t) & = \frac {t^3}3 + 10 \end{aligned}$

And displacement

$\begin{aligned} x(t) & = \int v(t) \ dt = \int \left(\frac {t^3}3 + 10 \right) dt = \frac {t^4}{12} + 10 t + C_2 \\ x(0) & = C_2 = 1 \\ \implies x(t) & = \frac {t^4}{12} + 10 t + 1 \\ x(10) & = \frac {10000}{12} + 100 + 1 \approx \boxed {934.3} \end{aligned}$