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Carnegie Mellon University

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Problem 44 Medium Difficulty

A train $4.00 \times 10^{2} {m}$ long is moving on a straight track with a speed of 82.4 ${km} / {h}$ . The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.

Answer

$t = 68.1 \mathrm { s }$ is the time that the train block the crossing.

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Video Transcript

So we're gonna let the initial speed of the train the initial equal. We know it's 82.4 kilometers per hour, but we need to convert and we have essentially, we can say one meter per second for every 3.6 kilometers per hour and this is equaling 22.89 meters per second and we can say that the final speed of the last car in the trade. So this would be the final. This would be equally 16.4 kilometers per hour. Again, we're gonna simply multiply by one divided by 3.6 so one meters per second for every 3.6 kilometers per hour and this is equaling 4.55 meters per second. So we can say that then we know the length to be equaling 400 meters and we can say that then the length is equaling T multiplied by the initial plus of the final divided by two. And so we can say that then this would be equaling brother. Better yet, we could solve her tea because it's we're trying to find, and this would be two times the length divided by the sum of the velocities. And so this is equaling two times 400 meters and then divided by 22.89 plus 4.55 The units here are meters per second and we find that Ty's equaling 29.2 seconds. This would be our final answer. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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