A spaceship travels in space at a constant speed of 1 260 km/h. How many metres does it travel in one tenth of a second?

Introduction / Context:

Here we apply speed conversion and the distance formula in a context involving a spaceship. The question gives a high speed in kilometres per hour and asks for the distance covered in a very small time interval, one tenth of a second. This tests the ability to convert between kilometres per hour and metres per second and then apply distance = speed * time correctly.

Given Data / Assumptions:

• Speed of the spaceship = 1 260 km/h.
• Time interval considered = 1/10 second.
• One kilometre = 1 000 metres.
• One hour = 3 600 seconds.
• Motion is uniform at the given speed.

Concept / Approach:

We first convert the speed from km/h into m/s, using the standard conversion factor. Once we know the speed in metres per second, the distance travelled in any time interval in seconds is computed as distance = speed * time. Since the time is 1/10 second, we simply multiply the speed in m/s by 0.1. Finally, we compare the result with the given options to select the correct distance.

Step-by-Step Solution:

Verification / Alternative check:

We can also compute directly using definitions. In one hour the spaceship travels 1 260 km, which is 1 260 000 metres. In 3 600 seconds it therefore covers 1 260 000 metres. Distance per second is 1 260 000 / 3 600 = 350 metres. Then in 0.1 second the distance is 350 * 0.1 = 35 metres. This exactly matches our earlier calculation and confirms the result as 35 metres.

Why Other Options Are Wrong:

Option 126 metres would correspond to distance covered in roughly 0.36 seconds at 350 m/s. Option 36 metres is very close but slightly higher than 35 and would correspond to a slightly longer time than 1/10 second. Option 125 metres is far too large for such a short time at the given speed. Only 35 metres accurately reflects the distance travelled in one tenth of a second.

Common Pitfalls:

A common error is to multiply by 18/5 instead of 5/18 when converting from km/h to m/s, which produces a very large and incorrect speed. Some learners also forget that 1/10 second equals 0.1 second and accidentally treat it as 10 seconds. Misplacing zeroes when converting kilometres into metres can lead to errors as well. Keeping track of units at every step helps prevent these mistakes.

Final Answer:

The spaceship travels 35 metres in one tenth of a second.