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I have two questions about this problem:

"A train slows down as it rounds a sharp horizontal turn, slowing from 90.0 km/h to 50.0 km/h in the 15. s(seconds) that it takes to round the bend. The radius of the curve is 150 m. Compute the acceleration at the moment the train speed reaches 50.0 km/h. Assume that it continues to slow down at this time at the same rate."

First question: I was able to solve the problem:

I converted the initial and final velocities from km/h to m/s, and then I found the tangential acceleration which = -0.714 m/s^2 and the radial acceleration which = 1.29 m/s^2. The magnitude was found easily and is equal to 1.48 m/s^2. The problem comes with the direction. To find the direction I found the inverse tangent of -0.741 divided by 1.29 and got -29.9(degrees) as a result. The book decides to divide the -0.741 as a positive 0.741 instead of negative. Is this an error on my part or the book's?

Second question: How do you know which quadrant the curve is in? The book has a picture of the train turning left (and it looks like going from the fourth quadrant into the first), but couldn't the train be bending to the right and possibly going from the first quadrant into the fourth?

Thank you for your time, and take care.

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# Homework Help: Radial and Tangential Acceleration of a train

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