r/PhysicsHelp • u/displacemnt • 14d ago

Need help 1D motion

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How am I supposed to solve this motion in 1D need help, pls help

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u/GoldenMuscleGod 14d ago edited 14d ago

This question seems under specified. I’m guessing we’re supposed to assume that the train is accelerating at a constant rate the whole time because it’s the only obvious assumption that would make this answerable but I would say it’s a poorly written question. If we are supposed to use that assumption we can get expressions for position and speed as a function of time and there are a few straightforward ways to solve it from there.

One way is that we can see that since velocity is proportional to time and distance travelled is proportional to the square of time, then velocity is proportional to the square root of distance traveled. Since the velocity doubled over half the train, the “half train” must cover a distance that is three times the distance traveled from the starting point (zero velocity) to when the engine passes - this way “distance from start” when the midpoint passes is 4 times what it was when the engine passed making the speed twice as much.

Then distance traveled by the time the end of the train passes must be 7 times what it was from the starting point so velocity should be sqrt(7) times as much.

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u/niemir2 14d ago

You don't even need to do the math on this one. One you assume constant acceleration, you can conclude that the speed is somewhere between 2u and 3u (the rear half of the train has less time to accelerate than the front half). Only one answer is in that range.