Ared train traveling at 72km/h and a green train traveling at 144km/h are headed towards each other along a straight, level track. when they are 950m apart, each engineer sees the other's train and applies the breaks. the breaks slow each train at the rate of 1.0m/s^2. is there a collision? if so, give the speed of the red train and the speed of the green train at impact, respectively. if not, give the separation between the trains when they stop.

given,

speed of red train = 72 km/h = 72× 0.278 = 20 m/s

speed of green train = 144 km/h = 144 × 0.278 = 40 m/s

deceleration of both the train = 1 m/s²

distance between the train when they start decelerating = 950 m

using equation of motion

v²  = u² + 2 a s

distance taken by the  red train to stop

v²  = u² + 2 a s

0 = 20² - 2×1×s

s = 200 m

distance taken by the  blue train to stop

v²  = u² + 2 a s

0 = 40² - 2×1×s

s = 800 m

so, both train will be cover 200 + 800 = 1000 m

hence, there will be collision between both the trains.

distance traveled by the green train will be 750 m

distance traveled by the red train will be 200 m

so, velocity of the red train will be zero

velocity of the green train will be

v²  = u² + 2 a s

v²  = 40² - 2 × 1× 750

v =  10 m/s

hence, velocity of the green train will be 10 m/s.

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