Train Speed Calculation Using Length and Time

To find the difference in the speeds of the two trains, we first need to calculate the individual speed of each train using the formula:

$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $

When a train passes a telegraph post, the distance covered is equal to the length of the train itself.

Calculating Speed of Train 1

• Given: Length ($L_1$) = 120 m, Time ($t_1$) = 10 s
• Calculation: Speed ($S_1$) = $L_1 / t_1$
• $ S_1 = \frac{120 \text{ m}}{10 \text{ s}} = 12 \text{ m/s} $

Calculating Speed of Train 2

• Given: Length ($L_2$) = 150 m, Time ($t_2$) = 15 s
• Calculation: Speed ($S_2$) = $L_2 / t_2$
• $ S_2 = \frac{150 \text{ m}}{15 \text{ s}} = 10 \text{ m/s} $

Difference in Train Speeds

• Objective: Find the magnitude of the difference between $S_1$ and $S_2$.
• Calculation: Difference = $|S_1 - S_2|$
• $ \text{Difference} = |12 \text{ m/s} - 10 \text{ m/s}| = 2 \text{ m/s} $

The magnitude of the difference in the speeds of the two trains is 2 m/s.