Answer:
Approximately , assuming friction between the vehicle and the ground is negligible.
Explanation:
Let denote the mass of the vehicle. Let denote the initial velocity of the vehicle. Let denote the spring constant (needs to be found.) Let denote the maximum displacement of the spring.
Convert velocity of the vehicle to standard units (meters per second):
.
Initial kinetic energy () of the vehicle:
.
When the vehicle is brought to a rest, the elastic potential energy () stored in the spring would be:
.
By the conservation of energy, if the friction between the vehicle and the ground is negligible, the initial of the vehicle should be equal to the of the vehicle. In other words:
.
Rearrange this equation to find an expression for , the spring constant:
.
Substitute in the given values , , and :
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4.0
∗
10 (26) W.
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