# Motion in one dimension

Homework Statement:
A train which connects city A to C, leaves the station A at 10:06 AM. The train accelerates for 6 minutes with a constant rate before it reaches its top speed. Then it is travelling with constant speed. Then it reduces its speed with a constant rate of 600 km/h² before it reaches the station of city C (The value of the speed is 0km/h when it reaches the station C). The train should arrive at city C at 10:42 AM. The distance between A to C is 60km

a) What is the acceleration of the train in the beginning ?
b) What is the maximum speed of the train ?
Relevant Equations:
X = Xo + Vot + 1/2 at²
V = Vo + at
V² - Vo² = 2aX
total time: t = 36 mins = 0.6h = t1 + t2
=> t2 = t - t1 = 0.6h - 0.1h = 0.5h

Vmax = a1 x t1
Vat C = Vmax + a2t2
substitute Vmax in Vat C we have : 0 = a1 x 0.1h + (-600 km/h²) x 0.5h => a1 = 3000km/h²
Vmax = a1 x t1 = 3000 x 0.1 = 300km/h

I check the result by:
x1 = ½ a
1 t1² = ½ . (3000). (0.1²) = 15km
x = ½ a
2t2² + vmaxt2 + x1 = ½ (-600).(0.5²) + (300).(0.5) + 15km = 90km

I don't know why the total distance when i check the result turn out to be 90km, while the questions states that AC is 60km

haruspex
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(-600 km/h²) x 0.5h
It is not slowing down for half an hour. It spends some unstated time at constant speed.

PeroK
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@hquang001 If I were you, I'd draw a speed vs time graph, where the distance is the area under the graph. It's easy to get lost if you only use the SUVAT equations.

It is not slowing down for half an hour. It spends some unstated time at constant speed.
This is the hint which i forgot to put in the question statement: It could be that you get more than one answer .

After considering your help and calculating again, i really got two possible maximum speed value like the hint stated I want to ask how i can check if my results are correct in situation like this, or in general, one dimensional motion ?

Last edited:
@hquang001 If I were you, I'd draw a speed vs time graph, where the distance is the area under the graph. It's easy to get lost if you only use the SUVAT equations.
I have done it again and also include a simple graph

This is the hint which i forgot to put in the question statement: It could be that you get more than one answer .

After considering your help and calculating again, i really got two possible maximum speed value like the hint stated View attachment 278640

PeroK
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Have you checked your solutions? Do they both work out?

Have you checked your solutions? Do they both work out?
Only one solution is possible
When i substitute V = 522.09 km/h to find t3,
t3 = 0.87h which will make t2 negative

PeroK
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Only one solution is possible
When i substitute V = 522.09 km/h to find t3,
t3 = 0.87h which will make t2 negative
Okay, so you have one good solution?

Okay, so you have one good solution?
Yes, Vmax = 137.91 is possible
but i don't know if it's correct or not, i don't know how to check it

PeroK
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