Answer
The red train's speed at impact is 0.
The green train's speed at impact is $10~m/s$
Work Step by Step
We can convert $72~km/h$ to units of $m/s$:
$(72~km/h)\times (\frac{1000~m}{1~km})\times (\frac{1~h}{3600~s}) = 20~m/s$
We can find the distance $x_r$ the red train requires while braking to a stop:
$v^2 = v_0^2+2ax_r$
$0 = v_0^2+2ax_r$
$x_r = -\frac{v_0^2}{2a}$
$x_r = -\frac{(20~m/s)^2}{(2)(-1.0~m/s^2)}$
$x_r = 200~m$
We can convert $144~km/h$ to units of $m/s$:
$(144~km/h)\times (\frac{1000~m}{1~km})\times (\frac{1~h}{3600~s}) = 40~m/s$
We can find the distance $x_g$ the green train requires while braking to a stop:
$v^2 = v_0^2+2ax_g$
$0 = v_0^2+2ax_g$
$x_g = -\frac{v_0^2}{2a}$
$x_g = -\frac{(40~m/s)^2}{(2)(-1.0~m/s^2)}$
$x_g = 800~m$
The trains require a total distance of 1000 meters to stop in time. Therefore, there is a collision, since the initial distance between the trains was only 950 meters.
The red train will come to a stop after 200 meters while the green train is still slowing down. Therefore the speed of the red train at impact is 0.
The impact occurs after the green train has traveled 750 meters. We can find the green train's speed at impact:
$v^2 = v_0^2+2ax_g$
$v = \sqrt{v_0^2+2ax_g}$
$v = \sqrt{(40~m/s)^2+(2)(-1.0~m/s^2)(750~m)}$
$v = 10~m/s$
The green train's speed at impact is $10~m/s$
