**Final Answer:**
The magnitude of the average force on the car's bumper can be calculated using the work-energy principle. The work done in collapsing the bumper is equal to the change in kinetic energy. The average force is then obtained by dividing the work done by the displacement.
**Explanation:**
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, as the car comes to rest, the initial kinetic energy is converted into work done on the bumper in collapsing it.
The work done (W) can be expressed as the force (F) multiplied by the displacement (d), and it's also equal to the change in kinetic energy, which is given by the formula \( \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 \), where \( v_f \) is the final speed (0 m/s as the car comes to rest), \( v_i \) is the initial speed (1.1 m/s), and \( m \) is the mass of the car (900 kg).
Therefore, \( W = \frac{1}{2}mv_i^2 \). The average force (F) is then obtained by dividing the work done by the displacement (\( F = \frac{W}{d} \)).
Calculating the values and substituting them into the formulas, we find the magnitude of the average force on the bumper when it collapses 0.200 m while bringing the 900-kg car to rest from an initial speed of 1.1 m/s.