1. Given data

• Mass of box: $m = 2\,\text{kg}$
• Applied force: $\vec F = (20\hat i + 10\hat j)\,\text{N}$
• Time: $t = 10\,\text{s}$
• Initial velocity: $u_x = 0$
• Surface is frictionless.

We need the displacement along the x-axis after $10\,$s.

2. Find acceleration along x-axis

Using Newton's second law along the x-direction: $F_x = ma_x$

Here, $F_x = 20\,\text{N}$ So, $a_x = \frac{F_x}{m} = \frac{20}{2} = 10\,\text{m/s}^2$

3. Use kinematics along x-axis

Since initial velocity along x is zero, $s_x = u_x t + \frac{1}{2} a_x t^2$

Substitute values: $s_x = 0 + \frac{1}{2}(10)(10^2)$ $s_x = 5 \times 100 = 500\,\text{m}$

4. Final answer

The displacement along the x-axis after $10\,$s is: $\boxed{500}$