A car of length 5 m moving at 20 m/s overtakes a truck of length 15 m moving at 15 m/s. Initially the front of the car is 10 m behind the rear of the truck. Overtaking is complete when the rear of the car is 10 m ahead of the truck's front. At the initial instant an oncoming car is 400 m from the overtaking car and moves at 25 m/s. What is the time margin between completion of overtaking and meeting the oncoming car?
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Question

A car of length 5 m moving at 20 m/s overtakes a truck of length 15 m moving at 15 m/s. Initially the front of the car is 10 m behind the rear of the truck. Overtaking is complete when the rear of the car is 10 m ahead of the truck's front. At the initial instant an oncoming car is 400 m from the overtaking car and moves at 25 m/s. What is the time margin between completion of overtaking and meeting the oncoming car?

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G1 Physics · Accepted Answer

Required relative gain on truck=10+15+5+10=40 m. Relative speed=5 m/s, so overtaking takes 8 s. The oncoming car closes on the overtaking car at 45 m/s, so meeting time=400/45=80/9 s. Margin=80/9−8=8/9 s.