What is the radius of curvature of the track at 6 seconds into the curve?

AI Thread Summary
To find the radius of curvature of the track at 6 seconds into the curve, the relationship between horizontal acceleration and radius must be utilized. Given the train's horizontal acceleration of 2 m/s², the formula for centripetal acceleration (a = v²/r) can be rearranged to solve for radius (r = v²/a). At 6 seconds, the train's speed can be interpolated between its initial and final speeds, allowing for the calculation of the radius using the average speed during that interval. The relevant equations for motion and acceleration are crucial for determining the radius of curvature accurately. This analysis highlights the importance of understanding the dynamics of motion in curved tracks.
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Homework Statement


A train enters a curved horizontal section of track at 100 km/hr and slows down with constant deceleration to 15 km/hr in 12 seconds. An accelerometer mounted inside the train measures a horizontal acceleration of 2 m/s^2 when the train is 6 seconds into the curve. Calculate the radius of curvature of the track for this instant.


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What are the relevant equation? How is radius of curvature related to the acceleration?
 
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