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Dynamics! help!

A subway train is being designed for operation between two stations A and B, which are 2 km apart.
If the maximum acceleration and deceleration are to be limited to 0.6g and the maximum velocity is to be
limited to 126 km/h, determine the minimum time for the train to make the trip from A to B.
Original post by Daylyt
A subway train is being designed for operation between two stations A and B, which are 2 km apart.
If the maximum acceleration and deceleration are to be limited to 0.6g and the maximum velocity is to be
limited to 126 km/h, determine the minimum time for the train to make the trip from A to B.


Post your working so far so we can help.
Reply 2
Original post by Smack
Post your working so far so we can help.


126 km/hr / 3.6 = 35 m/s. Use kinematic equation for the time it takes for the train to reach its maximum speed (v=u+at) 35=0+0.6(9.8)t, hence t = 5.95sec, then used another equation to get the distance it took to reach maximum speed at it gave me 26.1 m. I can't progress and don't even know whether this is the correct approach, any help appreciated, thanks!
Original post by Daylyt
126 km/hr / 3.6 = 35 m/s. Use kinematic equation for the time it takes for the train to reach its maximum speed (v=u+at) 35=0+0.6(9.8)t, hence t = 5.95sec, then used another equation to get the distance it took to reach maximum speed at it gave me 26.1 m. I can't progress and don't even know whether this is the correct approach, any help appreciated, thanks!


I would divide the journey into three parts: a first part with acceleration, a middle part with constant velocity, and a third part with deceleration. For simplicity, the third part can be said to be the reverse of the first part.

I agree with what you have done so far (although I would recheck your distance), and you have already effectively worked out the third part, too.

You know the speed the train travels during the constant velocity section, and you can work out the distance it travels. Then work out the time and you're golden.

PS You know your final answer should be in the region of a minute, as you have a train travelling over a distance of 2 km at a speed of ~120 km/hr.
(edited 7 years ago)

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