1-dimensional kinematics - final velocity of 2 trains in opposing direction

[syllll_213]

Homework Statement

A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each other along a straight, level track. When they are 950 m apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 m s2. Is there a collision?
If so, answer yes [in the first box] and give the speed of the red train and the speed of the green train at impact, respectively. [in the second and third box - give answers as integers, and in units: m/s but without the units]
If not, answer no [in the first box] and give the distance travelled by the red train and the distance travelled by the green train when they stop, respectively. [in the second and third box - give answers as integers in units m but without the unit]

Relevant Equations

v = d/t
2ad = v^2 -v0^2

Hi, so I first converted the speeds to meters per second (m/s), and then proceed to finding if they will clash using 2ad = v^2 - v0^2 assuming v0^2 is zero to find their final position.

Red train speed: 20 m/s
Green train speed: 40 m/s

The stopping distance d for red train is 200 m and the stopping distance from Green train is 800m. Since they add up to 1000m > 950m, they would clash.

However, when I try to find out the distance they travel, I fail. I tried to use x(t)1 + | x(t)2| = 950, but the modulus has complicated the whole thing and I ended up with no solution.

 

[jbriggs444]

However, when I try to find out the distance they travel, I fail. I tried to use x(t)1 + | x(t)2| = 950, but the modulus has complicated the whole thing and I ended up with no solution.

If the modulus is giving you troubles, get rid of it.

What is your formula for $x_1(t)$?
What is your formula for $x_2(t)$?
Is $x_2(t)$ positive? Or negative?
Is the absolute value of $x_2(t)$ equal to $x_2(t)$ or to $-x_2(t)$?

 

[PeroK]

You have to be careful with a problem like this. The red train will stop before the green train. At that point, I assume, the train remains at rest. The acceleration of $-1 m/s^2$ does not continue past that point. The motion of the red train may need to be split into two stages.

 

[Orodruin]

You have already concluded the answer is ”yes, they collide”. So the thing you need to answer now is the speeds at impact.

Note that the red train stops in half the time of the green. This should make you have some suspicion about the state of motion of the red train at impact* and also tell you how far the green train needs to move to find its final speed.

* Checking where the green train is when the red train stops will confirm this.