Answer:
The distance between the two trains at the instant the moving train began to brake was 460.74 m.
Explanation:
Hi there!
The equations of position and velocity of the moving train are the following:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position of the train at a time t.
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
v = velocity of the train at a time t.
Let's place the origin of the frame of reference at the point where the train starts slowing down so that x0 = 0.
Using the equation of velocity, we can calculate the acceleration of the train:
v = v0 + a · t
When the train stops at t = 48.3 s its velocity is zero. Then:
0 = v0 + a · t
-v0 / t = a
v0 = 68.5 km/h · (1000 m / 1 km) · (1 h / 3600 s) = 19.0 m/s
t = 48.3 s
a = -19.0 m/s / 48.3 s
a = -0.393 m/s²
Now that we have the acceleration, we can find the position of the train after the 48.3 s it takes the train to stop:
x = x0 + v0 · t + 1/2 · a · t² (x0 = 0 because the origin is the initial position)
x = 19.0 m/s · 48.3 s - 1/2 · 0.393 m/s² · (48.3 s)²
x = 459.29 m
The train traveled 459.29 m and stopped at a distance of 1.45 m from the other train. So, the distance between the two trains at the instant the moving train began to brake was (459.29 m + 1.45 m) 460.74 m.
