A train moves past a telegraph post and a 264 m long bridge in 8

SOLUTION

Concept:

• Speed is defined as the ratio of distance travelled to that of time taken.
• Velocity is defined as the ratio of displacement to that of time taken.
• Speed is scalar whereas Velocity is a vector quantity.

\(speed = \frac{{distance}}{{time}}\)

Calculation:

Given that two cases of the train but train speed will be constant in both cases. So, by equating speed we get the length of the train first.

Consider ‘l’ as the length of the train.

Case (i)

Train crossing telegraph post in 8 sec.

Distance covered = l m

Time taken = 8 sec

\(s = \frac{l}{8}\;m/s\)

Case (ii)

Train crosses bridge of length = 264 m

Total length = l + 264 m

Time taken = 20 sec

\(S = \frac{{l + 264}}{{20}}\)

From case (i) and case (ii), the speed of the train is the same.

\(\frac{l}{8} = \frac{{l + 264}}{{20}}\)

\(\frac{l}{2} = \frac{{l + 264}}{5}\)

5l = 2l + 528

3l = 528

l = 176 m

From case (i) we get the speed as:

\(s = \frac{{176}}{8}\;m/s\)

S = 22 m/s

Converting Meter/Sec to Km/Hour

S = (22 × 18)/5

S = 396/5

S = 79.2 Km/hour