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During a car crash test, a car of mass $1200\text{ kg}$ is sent down a horizontal track at a constant velocity of $30\text{ m/s}$. The car strikes a barrier that compresses until the car comes to a stop. This is very similar to a compressed spring. If the car comes to a stop in $0.25\text{ seconds}$ and the spring compresses $1.75\text{ m}$, what power was needed to stop the car AND what was the spring constant of the barrier?

A

$k=352{,}700 \text{ N/m}$; $P=540{,}000 \text{ W}$

B

$k=617{,}100 \text{ N/m}$; $P=2{,}160{,}000 \text{ W}$

C

$k=617{,}100 \text{ N/m}$; $P=540{,}000 \text{ W}$

D

$k=352{,}700 \text{ N/m}$; $P=2{,}160{,}000 \text{ W}$

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