Passing of a train I

A passenger train of length $$L=120\,\mathrm{m}$$ travels at a speed of $$v=30\,\mathrm{\frac{km}{h}}$$. How long does it take the train to pass:

a)  a power pole?

b)  a platform of length $$d=50\,\mathrm{m}$$?

• Hint 1:

Think of what distance the locomotive of the train has to travel so that the whole train passes the pole or the platform.

Draw a picture for both cases.

• Hint 2:

You know the distance which the locomotive has to travel and its speed. The desired times can be found easily.

Make sure that all the assigned quantities are in the base units.

• Complete Solution a)

a) Suppose that the width of the pole is very small compared with the length of the train. Before the whole train passes the pole, the locomotive has to travel the distance equal to the length of the train, i.e. L.

It travels this distance in the time:

$t_{1}\,=\,\frac{L}{v}\,=\,\frac{120}{8{,}3}\,\mathrm{s}\,=\,14.4\,\mathrm{s}.$
• Complete Solution b)

b) We cannot consider the width of the platform insignificant, we have to take it into account. In order for the whole train pass the platform, the locomotive has to travel the length of the train L (so the whole train passes the beginning of the platform) and the length of the platform d (the whole train passes the whole platform).

It travels this distance in the time:

$t_{2}\,=\,\frac{L+d}{v}\,=\,\frac{120+50}{8.3}\,\mathrm{s}\,=\,20.4\,\mathrm{s}$
The passenger train passes the power pole in $$14.4\,\mathrm{s}$$. The train passes the platform in $$20.4\,\mathrm{s}$$.