A red train traveling at 72 km/h and a green train traveling at 144 km/h are hea

Question

A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 880 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, give (a) the speed of the red train, (b) the speed of the green train, and (c) the separation between the trains when they collide (0 m).
If not, give (a) the speed of the red train (0 m/s), (b) the speed of the green train (0 m/s), and (c) the separation between the trains when they stop.

Explanation / Answer

Red train's speed = 72km/h = 72000/3600 m/s = 20 m/s

Using v = u + at, we get 0 = 20 - 1*t or t = 20 s

Dist. travelled = ut + 0.5at^2 = 20*20 - 0.5*1*400 = 200m

A little thought on proportionality will show that since the speed is double and a is the same for the green train, the time the green train will take to come to a stop will be 2*20s and the distance needed to come to a stop will be (2^2)*200m

Thus for the green train, t = 40s & dist.travelled = 800m

So the trains will collide.

The red train would obviously have stopped after 200m but the green train would collide, the speed of the collision given by the equation
v^2 = u^2 + 2as or v^2 = 40^2 -2*750 = 100

Thus speed of the green train at collision = 10 m/s

Ans:(a) the trains will collide
(b) the speed at cpllision will be 10 m/s for the green train. The red train would have stopped

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