A train is travelling at the speed of 180 km/hr. In order to trap superman Lex Luthor has broken the tracks. Unware of Luthor's evil intensions, superman tries to stop the train by pushing it in opposite direction.Right at the moment when the train is 300 m away from the crack in the track, Superman is applying a deceleration of 5 m/s2. Just after 2 sec a bullet laced with kryptonite hits superman which incapacitates him for a while. How long has super man got to remove the bullet and start to give deceleration so to protect the innocents? (Trains brake system has failed)
Trains initial velocity = 180 km/hr
To convert km/hr → m/s
To convert m/s in km/hr
u = 50 m/s
Superman a = −5m/s2
bullet hits after 2 sec so till 2 a = -5 m/s
t = 2 sec
s=ut+12at2 ; v = u + at
v = 40 m/s
Now super man is down.He is trying to remove bullet, Lets assume he takes time t.so the distance moved by train = v = st⇒s2=40t as no accelaration is present.
Now superman is back in action and let's assume he manages to stop the train just before the crack.
So total distance was 300 m
Train has moved s1+s2=90+40t
So distance left to cover = 300 - 90 - 40t = 210 - 40t
u = 40 m/s for this journey
a = −5m/s2
v = 0 m/s ← as train is stopping
-1600 = 2(-5). (210 - 40t)
160 = 210 - 40t
So superman has 1.25 sec to remove his bullet.