A train 100m long moving on a straight level track passes a pole in 5s. Find (a) the speed ofthe train (b) the time it will take to cross a bridge 500m long

1. Break Down the Problem

We need to find:

1. The speed of the train as it passes a pole.
2. The time it will take for the train to cross a bridge that is 500 m long.

2. Relevant Concepts

• Speed is calculated using the formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
• When passing a bridge, the train will need to cover both its own length and the length of the bridge.

3. Analysis and Detail

Part (a): Finding the Speed of the Train

• The length of the train is 100 m, and it passes a pole in 5 seconds.
• Using the formula for speed: $\text{Speed} = \frac{100 \, \text{m}}{5 \, \text{s}} = 20 \, \text{m/s}$

Part (b): Finding the Time to Cross a Bridge

• The total distance to cover when crossing the bridge is the length of the train plus the length of the bridge: $\text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} = 100 \, \text{m} + 500 \, \text{m} = 600 \, \text{m}$
• The speed of the train is 20 m/s. Using the formula for time: $\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{600 \, \text{m}}{20 \, \text{m/s}} = 30 \, \text{s}$

4. Verify and Summarize

• The calculations have been checked, and the values align with the formulas used.

Final Answer

(a) The speed of the train is $20 \, \text{m/s}$.
(b) The time it will take to cross the bridge is $30 \, \text{s}$.