Train Collision Calculation: Red Train vs Green Train on 950 km Track"

[brendan3eb]

Homework Statement

A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward one another along a straight, level track. When they are 950 km apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 1.0 m/s^2. Is there a collision? If so, what is the speed of each train at impact? If not, what is the separation between the trains when they stop?

Homework Equations

x=x0 + v0T + (1/2)(x - x0)

The Attempt at a Solution

I tried using the above equation, but I could not get a reasonable answer. I changed everything to meters and seconds. Here are the changes for those units:

95 km = 950,000 m
221 km/h = 61.39 m/s

 

[xRadio]

Just split it into two equations, and find the distance it takes to stop each one.

 

[m2003]

144 km/h = 40 m/s
1.0 m/s^2 = 1 m/s^2

I would approach this problem by first breaking it down into smaller components and identifying the relevant equations and variables.

First, I would draw a diagram of the situation to visualize the problem. The red and green trains are traveling towards each other on a straight, level track. The initial separation between them is 950 km.

Next, I would identify the relevant equations that can help me solve this problem. The first equation that comes to mind is the equation for position, which is x = x₀ + v₀t + 1/2at². This equation relates the final position (x), initial position (x₀), initial velocity (v₀), acceleration (a), and time (t).

In this case, we know the initial position (950 km), initial velocity (72 km/h and 144 km/h), and acceleration (1.0 m/s²). We are trying to find the final position (separation between the trains when they stop) and time (until they stop).

To solve for the final position, we can use the equation x = x₀ + v₀t + 1/2at², where x is the final position, x₀ is the initial position (950 km), v₀ is the initial velocity, and a is the acceleration. We can set up two equations, one for each train, and solve for the time (t) when the trains will stop.

For the red train:
x = 950,000 m + (72 km/h)(1000 m/1 km)(t) + 1/2(1.0 m/s²)(t²)
x = 950,000 m + (72,000 m/h)(t) + 0.5(t²)

Similarly, for the green train:
x = 950,000 m + (144 km/h)(1000 m/1 km)(t) + 1/2(1.0 m/s²)(t²)
x = 950,000 m + (144,000 m/h)(t) + 0.5(t²)

Now, we can set these two equations equal to each other and solve for t:
950,000 m + (72,000 m/h)(t) + 0.5(t²)