Does increasing the time interval over which the momentum of an object is brought to zero require you to use a larger or smaller force?
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Okay, let's think about this. When you increase the time interval, which is what is being done in this question, you are essentially taking longer to do what has to be done. If you have more time to achieve the same result, which would be bringing the momentum of the object to zero, you could use less force to achieve the same result.
Think about it this way; if you were driving a 2000 pound SUV, going 30 miles per hour, which would require more force, to stop in 3 seconds, or to stop in 9 seconds? The 3 second stop would certainly require more force, whereas the 9 second stop would require a smoother, less-stringent application of the braking force. More time equals less force required; go with the smaller force.
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