
Two trains each of length $50\,m$, are approaching each other on parallel rails. Their velocities are $10\,m/s$ and $15\,m/s$. They will cross each other in ?
Answer
163.2k+ views
Hint: First start with all the information provided in the question. Here the length of both the trains approaching each other are of equal length so this simplifies the process. Direction of both the trains is towards each other when they are approaching each other hence put the required symbol before their velocities.
Formula used:
The formula of total distance (D) incase two trains are travelling in the same direction is,
$D=2l$
Where, $l$ is the length of the one train.
Complete step by step solution:
Start with the given information from the question:
Length of both the train is $l = 50\,m$
Velocity of both the trains are;
First train’s velocity is $10\,m/s$.
Second train’s velocity is $15\,m/s$.
Now we have to find the distance that is
$D = 2l$
$\Rightarrow D = 2 \times 50 = 100\,m$
Now we have to find the relative velocity as the velocity of the second train is relative to the first train’s velocity. We know that relative velocity,
$v = {v_2} - ( - {v_1})$
$\Rightarrow v = 15 + 10 = 25$
We know that time is distance divided by speed,
$t = \dfrac{D}{v}$
Now put all the values from the above equations, we get;
$t = \dfrac{{100}}{{25}} = 4$
$\therefore t = 4\sec $
Therefore both the trains will cross each other in $4\sec $.
Note: Be careful about the direction of both the trains that is whether they are approaching to each other or are moving apart from each other because we have to put the required symbol as per the direction of the trains before putting the velocities of the train in the respective equations.
Formula used:
The formula of total distance (D) incase two trains are travelling in the same direction is,
$D=2l$
Where, $l$ is the length of the one train.
Complete step by step solution:
Start with the given information from the question:
Length of both the train is $l = 50\,m$
Velocity of both the trains are;
First train’s velocity is $10\,m/s$.
Second train’s velocity is $15\,m/s$.
Now we have to find the distance that is
$D = 2l$
$\Rightarrow D = 2 \times 50 = 100\,m$
Now we have to find the relative velocity as the velocity of the second train is relative to the first train’s velocity. We know that relative velocity,
$v = {v_2} - ( - {v_1})$
$\Rightarrow v = 15 + 10 = 25$
We know that time is distance divided by speed,
$t = \dfrac{D}{v}$
Now put all the values from the above equations, we get;
$t = \dfrac{{100}}{{25}} = 4$
$\therefore t = 4\sec $
Therefore both the trains will cross each other in $4\sec $.
Note: Be careful about the direction of both the trains that is whether they are approaching to each other or are moving apart from each other because we have to put the required symbol as per the direction of the trains before putting the velocities of the train in the respective equations.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Charging and Discharging of Capacitor

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line
