Classic Physics Problem - How Long Does it Take for a Train to Pass a Platform?
In this feature, we’ll walk you through how to solve one of the classic types of physics problems. After seeing a worked example, you’ll have the opportunity to try several similar problems on your own.
These types of problems are likely to appear on your next exam, so it’s a good idea to copy at least one example and solution into your physics notebook for future reference. If you are up for the challenge, copy the problem below into your notebook and try to solve it before reading the solution. If you can figure out to solve the problem without any help, you should be able to solve these types of problems on an exam.
Key Concepts
Constant velocity motion
Relative motion and reference frames
When the magnitude of an object's velocity is equal to its speed
When the magnitude of an object's displacement is equal to the distance it travels
Distance = speed × time
Total distance traveled when passing an object
Introduction In real-world transportation, understanding how long it takes for a train to pass a platform is essential for scheduling, safety, and design. This problem explores how motion in one dimension can be analyzed using simple kinematic relationships.
❓ Problem
A train that is 30 meters long travels at a constant velocity of 10 m/s. It passes completely by a 20-meter-long platform.
How long does it take for the entire train to pass the platform?
🧠 Before You Solve
When solving a physics problem, it’s often helpful to:
Put the problem into your own words
Draw a sketch of the situation
Identify what you know and what you’re solving for
Take a moment to do that in your notebook now.
📓 Note (Add to Your Notebook!)
Because the motion in this problem takes place in one dimension along a straight line, we can use the terms speed and velocity interchangeably. In this case, the magnitude of the velocity is equal to the speed.
Similarly, we can use distance and displacement interchangeably, since the magnitude of the displacement is equal to the distance the train travels.
1. Initial Conditions:
The initial time (to)and initial position (Xo) are measured when the front of the train reaches the start of the platform.
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2. Final Conditions:
The final time (t) and final position (X) are measured when the back of the train passes the end of the platform.
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3. Total Distance Traveled:
Since the entire train must clear the platform, the magnitude of the displacement or the total distance that the train must travel would be equal to ( ΔX =X−X0=50 m −0 m =50 m) 50 meters.
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🧮 Step-by-Step Solution
Let's use the five-step method to solve the problem.
❓ Additional problems to solve in your notebook
🚆 Displacement as the Unknown
A train travels at a constant velocity of 12 m/s and takes 6 seconds to completely pass a platform.
What is the magnitude of the train's displacement while passing the platform?🚆 Displacement as the Unknown
A train travels at a constant velocity of 15 m/s and takes 5 seconds to completely pass a platform.
What is the magnitude of the train's displacement while passing the platform?⏱️ Time as the Unknown
A 50-meter-long train passes a 30-meter-long platform while moving at 10 m/s.
How much time does it take for the train to pass the platform?⏱️ Time as the Unknown
A train that is 40 meters long passes a 35-meter-long platform at a constant velocity of 15 m/s.
How long does it take for the train to completely pass the platform?🏃 Velocity as the Unknown
A train passes a platform in 5 seconds. The train is 45 meters long, and the platform is 20 meters long.
What is the uniform velocity of the train?🏃 Velocity as the Unknown
A train that is 25 meters long passes a 15-meter-long platform in 5 seconds.
What is the train’s uniform velocity?🧮 Answer Key with Step-by-Step Solution
I hope that this was helpful. Good luck with your studies!
