Question

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/$s^2$. 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)

• A. 1s
• B. 2s
• C. 1.25s
• D. 0s

Answer 1

The correct option is C

1.25s

Trains initial velocity = 180 km/hr

= $180\times \frac{5}{18}=50m/s$

To convert km/hr $\to$ m/s

$\frac{180\times 1000m}{60\times 66sec}=180\times \frac{5}{18}=50m/s$

To convert m/s in km/hr

$\frac{50}{1000\times 60\times 60}=50\times \frac{18}{5}=180km/hr$

u = 50 m/s

Superman a = $-5m/s^2$

bullet hits after 2 sec so till 2 a = -5 m/s

t = 2 sec

$s=ut+\frac{1}{2}a{t}^2$ ; v = u + at

$s_1=90m$

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 = $\frac{s}{t}\Rightarrow s_2=40t$ 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 $s_1+s_2=90+40t$

So distance left to cover = 300 - 90 - 40t = 210 - 40t

u = 40 m/s for this journey

a = $-5m/s^2$

v = 0 m/s $\leftarrow$ as train is stopping

$v^2-u^2=2as$

-1600 = 2(-5). (210 - 40t)

160 = 210 - 40t

$t=\frac{5}{4}=1.25sec$

So superman has 1.25 sec to remove his bullet.