A missile travels at a constant speed of 1278 km per hour. Convert this speed into metres per second and determine how many metres the missile travels in one second.

Introduction / Context:
This is a straightforward unit conversion question that checks your ability to convert a speed given in kilometres per hour into metres per second. Such conversions are very common in physics, aptitude tests and real life engineering problems, so it is important to be comfortable with the underlying relationships between units.

Given Data / Assumptions:

• Speed of the missile = 1278 km per hour.

• 1 kilometre = 1000 metres.

• 1 hour = 3600 seconds.

• The speed is constant during the time interval considered.

Concept / Approach:
To convert from kilometres per hour to metres per second, we use the conversion factors between kilometres and metres and between hours and seconds. The basic method is to multiply by 1000 to convert kilometres to metres and then divide by 3600 to change hours into seconds. A useful combined factor that many students remember is that 1 km per hour equals (5 / 18) metres per second.

Step-by-Step Solution:
Given speed = 1278 km per hour. Use the relationship: 1 km per hour = 1000 metres / 3600 seconds. This simplifies to 1 km per hour = (5 / 18) metres per second. Therefore, speed in metres per second = 1278 * (5 / 18). First compute 1278 / 18 = 71. Now multiply by 5: 71 * 5 = 355. Thus, speed = 355 metres per second. So, in one second the missile travels 355 metres.

Verification / Alternative check:
Alternatively, perform the full unit conversion directly. Multiply 1278 km per hour by 1000 to convert to metres per hour: 1278 * 1000 = 1,278,000 metres per hour. Then divide by 3600 to get metres per second: 1,278,000 / 3600 = 355 metres per second. This confirms the earlier shortcut method using the factor 5 / 18 and shows both approaches are consistent.

Why Other Options Are Wrong:
The value 358 metres per second would result from a small arithmetic error, perhaps mis dividing by 18 or mis multiplying by 5. The value 345 metres per second is also close but incorrect and likely comes from rounding intermediate steps incorrectly. The value 313 metres per second is noticeably smaller and would indicate using an incorrect conversion factor. Only 355 metres per second exactly satisfies the conversion from 1278 km per hour using accurate arithmetic.

Common Pitfalls:
A typical mistake is to reverse the conversion and multiply by 18 / 5 instead of 5 / 18, which gives a very large and incorrect value. Another mistake is to forget either the 1000 or the 3600 factor when converting units step by step. Some students also round mid calculations and lose precision, which can move them away from the correct option in multiple choice questions. Always keep the relationship 1 km per hour = 5 / 18 metres per second in mind for quick and accurate conversions.

Final Answer:
The missile travels 355 metres in one second.