When does the jam start?

Classical Mechanics Level 3

Imagine a road with two cars, each of length \(L\). Car 1 gets on the road at \(t = 0\) moving at \(v_{1}\), and car 2 gets on the road at \(t = t_{2}\), moving at \(v_{2} > v_{1}\).

At what time does the front of car 2 to get in contact with the back of car 1?

Solve for the case where

\(v_{1} = 20\text{ m/s}, v_{2} = 25 \text{ m/s}, t_{2} = 100 \text{ s}\), and \(L = 5 \text{ m}\).

Express your answer in seconds.


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