Question

Two trains are moving at 50 m/s in opposite directions on the same track. The engineers see simultaneously that they are on a collision course and apply the brakes when they are 1,100 m apart. Assuming both trains have the same acceleration, what must this acceleration be (in m/s2) if the trains are to stop just short of colliding

Answer 1

Acceleration is 2.5 m/s^2

Step-by-step explanation:

Let train 1 travel x meters and train 2 travels 1000-x meters

As per the las of acceleration

`v^2 = u^2 + 2ax`

Substituting the given values, we get -

`0 = 50^2 + 2ax\\ax = -1250\\`---Eq (1)

Similarly

`0 = 50^2 + 2a(1000-x)\\a(1000-x) = 1250`-- Eq (2)

Substituting the value of ax from eq (1) into Eq(2), we get -

1000*a - 1250 = 1250

a = 2500/1000 = 2.5 m/s^2