Question

The driver of a train $A$ running at $25m{s}^{-1}$ sights a train $B$ on the same track with $15m{s}^{-1}$. The driver of train $A$ applies brakes to produce a deceleration of $1.0m{s}^{-2}$. If the trains are $200m$ apart, will the trains collide?

• A. yes
• B. no
• C. collision just avoided
• D. none of these

Answer 1

The correct option is C collision just avoided

First we need to find the time taken for A to reach B
Now, $u_{AB}=25-15=10m/s$

Put final velocity$=0$
$v_{AB}=u_{AB}+a_{AB}t=0$
$t=10s$

Now distance traveled by A in 10s
$s=ut+\frac{1}{2}a{t}^2\Rightarrow s=(25\times 10)-50=200m$

Thus collision just avoided.