Can a Man Catch a Constantly Accelerating Train?

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A man can catch a constantly accelerating train if his speed squared exceeds twice the product of the train's acceleration and the distance between him and the train. The discussion involves equating the distance formulas for both the train and the man, leading to a quadratic equation. Understanding the conditions for a physically meaningful solution of this quadratic is crucial. The hint suggests that analyzing the quadratic's discriminant will reveal the necessary conditions for the man to catch the train. This problem highlights the interplay between constant speed and constant acceleration in kinematic scenarios.
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:confused: Please help with this problem. A train moves from rest with const accel. a in a straight line. A man at distance b behind the train chases it with const. speed V. Show he can catch it if V^2 >2ab, and find when he does so.
I have found formulas for distance traveled for each and equated these but cannot understand where the Vsquared comes from.
Thanks to anyone who can help. Jess x
 
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Hint: When you equate those distance formulas you'll get a quadratic equation. What must be true for that quadratic to have a physically meaningful solution?
 

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