To find the net work done on the box, we can use the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy.

1. **Given Data**:
- Mass of the box \( m = 5 \, \text{kg} \)
- Acceleration \( a = 20 \, \text{m/s}^2 \)
- Time \( t = 7 \, \text{s} \)
- Initial velocity \( u = 0 \, \text{m/s} \)

2. **Calculate Final Velocity**:
The final velocity \( v \) can be calculated using the equation:
\[
v = u + at
\]
Substituting the values:
\[
v = 0 + (20 \, \text{m/s}^2)(7 \, \text{s}) = 140 \, \text{m/s}
\]

3. **Calculate Change in Kinetic Energy**:
The change in kinetic energy (\( \Delta KE \)) is given by:
\[
\Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2
\]
Since the initial velocity \( u = 0 \):
\[
\Delta KE = \frac{1}{2} m v^2
\]
Substituting the values:
\[
\Delta KE = \frac{1}{2} (5 \, \text{kg}) (140 \, \text{m/s})^2 = \frac{1}{2} \times 5 \times 19600 = 49000 \, \text{J}
\]

4. **Conclusion**:
The net work done on the box is:
\[
W = \Delta KE = 49000 \, \text{J}
\]

Thus, the net work done on the box is **49,000 J**.