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A car is traveling at a constant speed of 18.0 m/s, when the motorist sees a cow in the road 38.0 m ahead. If the maximum acceleration of the vehicle is -4.50 m/s^2, what is the maximum reaction time fo the motorist that will allow her to avoid hitting the cow?

I have tried many different ways. I was thinking you would use an integral from 0 to x because you want to find the maximum reaction time. The equation I thought to integrate was -38+18t+.5(-4.5)t^2 which, of course, was wrong. Please help!

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