Question

A red 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.

Answer 1

Answer:

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.