Question

A $100m$ long train moving on a straight level track passes a pole in $5s$. Find the speed of the train and the time it will take to cross a $100m$ long bridge.

• A. $13m{s}^{-1}$ and $40s$
• B. $25m{s}^{-1}$ and $30s$
• C. $15m{s}^{-1}$ and $65s$
• D. $20m{s}^{-1}$ and $10s$

Answer 1

The correct option is D $20m{s}^{-1}$ and $10s$

In the first case, train passes the pole in $5s$. This means that the distance train travels is equal to it's length $100m$ in $5s$.
Speed is defined as the ratio of distance travelled to time taken.

Speed of the train:
$v=\frac{100}{5}m{s}^{-1}=20m{s}^{-1}$

In the second case,
Distance to be covered by the train to cross a $100m$ long bridge is the sum of the length of train and the length of the bridge. Hence, distance travelled is given by:
$s=100+100=200m$
From formula of speed, time taken is given by:
$T=\frac{s}{v}$
or, $T=\frac{200}{20}=10s$