How Quickly Can a Train Accelerate on a Curve Without Exceeding Comfort Limits?

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SUMMARY

The discussion focuses on calculating the minimum time required for a train to accelerate from 250 km/h to 300 km/h on a curved track with a radius of 5 km, while ensuring that the total acceleration does not exceed 0.2g. The key equations used include total acceleration as the sum of tangential and radial acceleration, and the relationship between speed, initial speed, tangential acceleration, and time. The integration of tangential acceleration over a specified time period yields a change in speed of 13.89 m/s, but participants encounter difficulties in solving the resulting quadratic equation for time.

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  • Understanding of basic physics concepts such as acceleration and forces.
  • Familiarity with the equations of motion, particularly those involving acceleration and speed.
  • Knowledge of calculus, specifically integration techniques.
  • Concept of g-forces and their application in real-world scenarios like train acceleration.
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  • Study the principles of circular motion and how radial acceleration affects objects in motion.
  • Learn about the derivation and application of the equations of motion in physics.
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Students in physics or engineering disciplines, transportation safety analysts, and anyone interested in the dynamics of train acceleration on curved tracks.

quantumlight
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Homework Statement


Bob and Villie are able to tolerate acceleration of 0.2g, the driver wants to accelerate from 250km/h to 300 km/h on a curved piece of track, the radius of curvature is 5km, what is the minimum time the driver can use to change speed?


Homework Equations


total acceleration = tangential acceleration + radial acceleration
speed = initial speed + tangential acceleration x time

The Attempt at a Solution



given that total acceleration must not exceed 0.2g, radial acceleration increases as tangential acceleration decreases. So what i did was integrate tangential acceleration over a time period from x to y which should equal to the change in speed.

Integration (x to y) tangential acceleration dt = 13.89 m/s

i was hoping to eventually end up with an equation that goes m(x-y) = 13.89 and then solve for x-y but when i plug in the above equations in b for tangential acceleration, I get this extremely complicated and unsolvable quadratic formula if i attempt to express the equations in terms of t.

Anyone?
 
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Can you show us what you got? Then we can comment on whether you're on the right track.
 
quantumlight said:

Homework Statement


Bob and Villie are able to tolerate acceleration of 0.2g, the driver wants to accelerate from 250km/h to 300 km/h on a curved piece of track, the radius of curvature is 5km, what is the minimum time the driver can use to change speed?


Homework Equations


total acceleration = tangential acceleration + radial acceleration
speed = initial speed + tangential acceleration x time

The Attempt at a Solution



given that total acceleration must not exceed 0.2g, radial acceleration increases as tangential acceleration decreases. So what i did was integrate tangential acceleration over a time period from x to y which should equal to the change in speed.

Integration (x to y) tangential acceleration dt = 13.89 m/s

i was hoping to eventually end up with an equation that goes m(x-y) = 13.89 and then solve for x-y but when i plug in the above equations in b for tangential acceleration, I get this extremely complicated and unsolvable quadratic formula if i attempt to express the equations in terms of t.

Anyone?

how do you say that?
 

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