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

In summary, the radius of curvature of a track refers to the distance from the center of the circle to the outer edge of the track and is an important factor in track design. It can be measured by calculating the average distance between the center point and the edge of the track at multiple points along the curve. The ideal radius of curvature varies depending on the type of track and its intended use, and can affect the speed of vehicles or athletes by making turns tighter or allowing for higher speeds.
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Starwanderer1
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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?
 

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

What is the radius of curvature of a track?

The radius of curvature of a track refers to the radius of the circular arc formed by the inner edge of the track. It is the distance from the center of the circle to the outer edge of the track.

Why is the radius of curvature important in track design?

The radius of curvature is an important factor in track design because it determines how sharp the turns in the track will be. A smaller radius of curvature means tighter turns, which can affect the speed of the vehicles or athletes using the track.

How is the radius of curvature measured?

The radius of curvature can be measured in several ways, depending on the type of track. In general, it can be calculated by measuring the distance between the center point of the track and the edge of the track at multiple points along the curve and then taking the average of these measurements.

What is the ideal radius of curvature for a track?

The ideal radius of curvature for a track depends on the type of track and its intended use. For example, a Formula 1 race track would have a much smaller radius of curvature than a high school track used for track and field events.

How does the radius of curvature affect the speed of vehicles or athletes on a track?

The radius of curvature can affect the speed of vehicles or athletes on a track in a few ways. A smaller radius of curvature can make it more difficult for vehicles or athletes to maintain high speeds, as it requires tighter turns. Additionally, a larger radius of curvature can allow for higher speeds, but may also increase the risk of accidents due to the potential for vehicles or athletes to lose control on longer, straighter sections of the track.

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