What is the length of a train running at a speed of 108 km per hour crosses a pole in 32 seconds?

The Unexpected Physics of a Passing Train

We often encounter seemingly simple problems that, upon closer inspection, reveal surprising insights into the fundamental principles of physics. Consider this: a train speeds past a stationary pole at 108 km/h, taking 32 seconds to complete the pass. How long is the train?

The immediate instinct might be to simply multiply the speed and time. After all, distance equals speed multiplied by time (d = st), a cornerstone of kinematics. And indeed, this straightforward calculation yields an answer:

108 km/h * (32 seconds) = ?

However, a direct multiplication won’t work. The units are incompatible. We need to convert either the speed to meters per second or the time to hours. Let’s convert the speed to meters per second:

108 km/h (1000 m/km) (1 h/3600 s) = 30 m/s

Now, we can perform the calculation:

30 m/s * 32 s = 960 m

Therefore, the train is 960 meters long.

This simple problem highlights a crucial point: the correct application of units is paramount in physics. Without consistent units, the calculation is meaningless. This seemingly trivial step underpins the accuracy of more complex calculations and the interpretation of experimental data.

Furthermore, the problem subtly touches on the concept of relative motion. The train’s speed is relative to the stationary pole. If the pole were moving, the calculation would become significantly more complex, requiring consideration of the pole’s velocity and its direction relative to the train.

This seemingly mundane observation of a train passing a pole offers a valuable lesson. It underscores the importance of careful unit conversion and the inherent principles of relative motion, reminding us that even seemingly simple problems can harbor significant underlying physics. The next time you see a speeding train, remember the 960 meters that encapsulate not just its length, but also a foundational principle of physics in action.