Question

A train \[100\;{\rm{m}}\]long is moving with a velocity of \[60\;{\rm{km}} \cdot {{\rm{h}}^{{\rm{ - 1}}}}\]. Find the time it takes to cross the bridge \[1\;{\rm{km}}\] long.

Answer 1

Hint: The above problem can be resolved using the concept and fundamentals of the linear kinematic and the motion in one-dimension. In this problem, we are given a train of some length and it is moving with some magnitude of velocity, such that it crosses a bridge. Then we need to find the time required by train to cross that bridge. So, to do so, we can apply the formula for the speed in linear kinematics. In this formula, the total length, including the length of the bridge and the length of the train is considered, and then the value is divided with the magnitude of velocity.

Complete step by step answer:
Given:
The velocity of train is, \[v = 600\;{\rm{km/h}} = 60\;{\rm{km/h}} \times \dfrac{{5/18\;{\rm{m/s}}}}{{1\;{\rm{km/h}}}} = 16.67\;{\rm{m/s}}\].
The length of the train is, \[{L_1} = 100\;{\rm{m}}\].
The length of bridge is, \[{L_2} = 1\;{\rm{km}} = 1\;{\rm{km}} \times \dfrac{{1000\;{\rm{m}}}}{{1\;{\rm{km}}}} = 1000\;{\rm{m}}\].
 The mathematical expression for the time taken to cross the bridge is given as,
\[t = \dfrac{{{L_1} + {L_2}}}{v}\]
Solve by substituting the value in the above equation as,
\[\begin{array}{l}
t = \dfrac{{{L_1} + {L_2}}}{v}\\
\Rightarrow t = \dfrac{{100\;{\rm{m}} + 1000\;{\rm{m}}}}{{16.67\;{\rm{m/s}}}}\\
\Rightarrow t \approx 66\;{\rm{s}}
\end{array}\]
Therefore, the time required to cross the bridge is 66 seconds.

Note:
To resolve the given problem, one must be able to understand the concept and all the fundamentals of motion in one-dimension. The motion in one -dimension implies that all the necessary variation, along with the velocity and acceleration, is needed to take place along the single direction in space. Moreover, there are several laws under the motion in one-dimension, which is required to be analysed and used accordingly with the condition.