Train Speed Difference Problem

This problem asks us to calculate the magnitude of the difference in speeds between two trains. We are given the time taken by each train to completely pass a telegraph post and their respective lengths. Understanding how a train passes a telegraph post is crucial for solving this train speed problem.

Understanding Train Motion Past a Post

When a train completely passes a telegraph post (or any point object), the distance the train travels is equal to its own length. The telegraph post itself is considered to have negligible dimensions. We will use the fundamental relationship between speed, distance, and time:

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

Let's denote the length of the train as the distance covered and the given time as the time taken.

Calculating First Train's Speed

For the first train, we are given its length and the time it takes to pass the telegraph post.

• Length of the first train ($\text{L}_1$) = $120 \, \text{m}$
• Time taken by the first train ($\text{T}_1$) = $10 \, \text{s}$

The distance covered by the first train is its length, $\text{D}_1 = \text{L}_1 = 120 \, \text{m}$.

Now, let's calculate the speed of the first train ($\text{S}_1$):

$\text{S}_1 = \frac{\text{D}_1}{\text{T}_1} = \frac{120 \, \text{m}}{10 \, \text{s}} = 12 \, \text{m/s}$

So, the speed of the first train is $12 \, \text{m/s}$.

Calculating Second Train's Speed

Similarly, for the second train, we have its length and the time it takes to pass the telegraph post.

• Length of the second train ($\text{L}_2$) = $150 \, \text{m}$
• Time taken by the second train ($\text{T}_2$) = $15 \, \text{s}$

The distance covered by the second train is its length, $\text{D}_2 = \text{L}_2 = 150 \, \text{m}$.

Now, let's calculate the speed of the second train ($\text{S}_2$):

$\text{S}_2 = \frac{\text{D}_2}{\text{T}_2} = \frac{150 \, \text{m}}{15 \, \text{s}} = 10 \, \text{m/s}$

So, the speed of the second train is $10 \, \text{m/s}$.

Magnitude of Speed Difference

The question asks for the magnitude of the difference in the speeds of the two trains. The magnitude refers to the absolute value of the difference, ensuring the result is positive.

Speed of the first train ($\text{S}_1$) = $12 \, \text{m/s}$

Speed of the second train ($\text{S}_2$) = $10 \, \text{m/s}$

Difference in speeds = $|\text{S}_1 - \text{S}_2|$

Difference in speeds = $|12 \, \text{m/s} - 10 \, \text{m/s}|$

Difference in speeds = $|2 \, \text{m/s}|$

Difference in speeds = $2 \, \text{m/s}$

The magnitude of the difference in the speeds of the two trains is $2.0 \, \text{m/s}$.

Therefore, the magnitude of the difference in their speeds is $12 \, \text{m/s} - 10 \, \text{m/s} = 2 \, \text{m/s}$.