Final answer:
Using the work-energy principle and given values, the calculated magnitude of the average force applied to the car's bumper is 2697.5 N, which is not one of the provided answer options.
Step-by-step explanation:
To calculate the magnitude of the average force exerted on a car's bumper when it collapses, we can use the work-energy principle. The principle states that the work done by forces on an object equals its change in kinetic energy (Work = ΔKE). The work done by the force when the bumper collapses is equal to the force times the distance over which it acts (Work = Force x Distance). Since the car comes to rest, its final kinetic energy is zero, and the initial kinetic energy can be calculated using ½ mv², where m is the mass and v is the speed.
We are given that the car's mass (m) is 900 kg and its initial speed (v) is 1.1 m/s. Hence, the initial kinetic energy (KE initial) is ½ * 900 kg * (1.1 m/s)². Then, the work done by the bumper is the negative of this kinetic energy, because it is removing the car's kinetic energy. This work is also equal to the force F times the distance over which the bumper collapses (0.200 m).
Therefore, we have:
Work = -KE initial
= -½ * 900 kg * (1.1 m/s)²
= -539.5 J
And since Work = Force x Distance:
-539.5 J = F * 0.200 m
F = -539.5 J / 0.200 m
F = -2697.5 N (The negative sign indicates the force is in the opposite direction of the motion)
The magnitude of the force, ignoring the sign, is therefore 2697.5 N, which is not one of the options provided. The options may be based on a different interpretation or different given values, and thus the correct answer from the given options could not be determined based on the current calculation.