A highspeed train with a constant speed of 234 km/h runs through a 620 m long tunnel, the train's length is 160 m.
What is the time interval to cross the tunnel?
Problem Data

train speed: v = 234 km/h;

train length: L = 160 m;

tunnel length: L_{T} = 620 m.
Problem diagram
The train has, a dimension essential to the problem, it is a large object.
It begins to cross the tunnel when the front of the train arrives at the tunnel entrance and ends when the rear of the
train arrives at the tunnel exit (figure 1).
We choose a frame of reference oriented to the right. The problem can be reduced to a particle, which represents the
rear of the train, at the origin of the frame (
S_{0}=0) with speed
v=234 km/h, and a point
given by the sum of train and tunnel lengths
\( S=L+L_{\text{T}}=160+620=780\;\text{m} \)
representing the tunnel exit.
Solution
First, we convert the speed of train given in kilometers per hour (km/h) to meters per second (m/s) used in the
International System of Units (
S.I.)
\[
v=234\;\frac{\cancel{\text{km}}}{\cancel{\text{h}}} \times \frac{1000\;\text{m}}{1\;\cancel{\text{km}}} \times \frac{1\;\cancel{\text{h}}}{3600\;\text{s}}=\frac{234}{3,6}\;\frac{\text{m}}{\text{s}}=65\;\text{m/s}
\]
The particle travels with constant speed, writing the equation of displacement as a function of time, we have
\[ \bbox[#99CCFF,10px]
{S=S_{0}+vt}
\]
\[
780=0+65\;t\\
65\;t=780\\
t=\frac{780}{65}
\]
\[ \bbox[#FFCCCC,10px]
{t=12\;\text{s}}
\]