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

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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?