Answer:
the minimum time between the two stations t = s/v + v/a
Explanation:
this is a problem of kinematics, we will divide it in part to solve it more easily, one part is when it is accelerated and another when it is at constant speed
Let's start when it has acceleration, tell us what part of the rest
Vf = Vo + at
Vf = a t
S
ince the maximum speed is "v", let's calculate the time it takes to reach this speed
t = v / a
Let's call this time t1
Let's look for the time it takes to slow down when it reaches the other station
0 = v + (-a) t
.t = v / a
Let's call this time t2
Now we have all the times of the accelerated movement we can calculate how far they travel in these times.
Starting X = Vo t + ½ a t² = 0 + ½ a t²
X1 = ½ a (v / a)²
X1 = v² / 2 a
Braking x = Vot + ½ a t² =
X2 = v (v / a) - ½ a (v / a)²
X2 = v² / a - ½ v² / a
X2 = v² / 2 a
The same distance
Let's calculate the distance you travel at constant speed
X3 = Xt -x1-x2
X3 = s -v² / 2 a -v² / 2 a
X3 = s -v² / a
We can calculate the time it takes to travel this distance
V = x / t
t = x / v
t3 = (s- v² / a) / v
t3 = s/v - v/a
Total travel time is
t all = t1 + t2 + t3
t all= v / a + v / a + (s / v -v / a)
t all= s/v + v/a
This is the minimum time between the two stations
