When and at what distance does the second train reach its maximum speed?

[fatteingenting]

A train starts out from Stavanger at 8.14 (exactly), in direction of Kristian- sand. It goes with constant speed 80.0 km/h until Sandnes, a distance of 15.0 km. Then it accelerates (instantaneously) to 120 km/h and proceeds towards Kristiansand. Kristiansand is 250 km from Stavanger.
A second train starts out from Kristiansand at 9.28 (exactly), direction Stav- anger. The driver immediately falls asleep with his foot on the accelerator, and the train accelerates at a constant rate of 0.100 m/s2, until it reaches the maximum speed of 160 km/h. It then accelerates no longer, but continues towards Stavanger at that maximum speed.

b) At what time, and at which distance from Kristiansand does the second train reach the maximum speed?

I know that the train uses 5760 s to reach max speed (t=(160km/h-0km/h)/0.100 m/s^2)
But how do I calculate the distance?


I tried s=1/2at^2, but that was wrong...

 

[Orodruin]

I tried s=1/2at^2, but that was wrong...

This would be the traveled distance, not the distance remaining to the destination.

 

[BvU]

Hello fatte, and welcome to PF.
You say s=1/2at^2, but that was wrong. What did you get as answer and why is it wrong ?
@Odor: the train starts at K and the question is "at which distance from K", so what is wrong with the traveled distance ?

 

[jbriggs444]

I know that the train uses 5760 s to reach max speed (t=(160km/h-0km/h)/0.100 m/s^2)

How is that again? 5760 seconds times 0.100 meters/second² is 576 meters/second. That's much faster than 160 km/hour.

 

[haruspex]

I know that the train uses 5760 s to reach max speed (t=(160km/h-0km/h)/0.100 m/s^2)

That's not the time I get from that calculation. What's 160km/h in m/s?

 

[BvU]

My guess is fatte saw the light and forgot to tell us. Either that, or he/she has fallen asleep (like the driver).

Railroad folks will reassure us that this exercise is completely unreal. Even dropping dead on top of the accelerator will quickly (50, 60 sec) cause the train to come to an uncomfortable emergency stop. Anyone care to explain ?

 

[toad22]

Continuing this problem, can someone help with this question?:
d) Where, when and at what relative speed do the two trains collide?

 

[NascentOxygen]

My guess is fatte saw the light and forgot to tell us. Either that, or he/she has fallen asleep (like the driver).

Railroad folks will reassure us that this exercise is completely unreal. Even dropping dead on top of the accelerator will quickly (50, 60 sec) cause the train to come to an uncomfortable emergency stop. Anyone care to explain ?

There's a console button that must be pressed when a buzzer sounds every few minutes/whenever. Failing this it's assumed the loco is driverless and the whole kit & caboodle grinds to a halt.

 

[BvU]

Toad appears to know something we don't know yet: that the trains are on one and the same track ?

If so, what have you worked out thus far ?

(all this provided the forum allows this kind of continuation...)