Introduction / Context:
This question tests the ability to convert speeds given in kilometres per hour into distances covered in very short time intervals measured in seconds. The object here is a spaceship traveling at 1260 km/h, and we are asked how many metres it travels in one tenth (1/10) of a second. This is a classic unit conversion problem in the time, speed and distance chapter.
Given Data / Assumptions:
- Speed of the spaceship = 1260 km/h.
- Time interval considered = 1/10 of a second.
- We need the distance covered in metres during this small time interval.
- The speed is constant throughout the time interval.
Concept / Approach:
We use the distance formula:
distance = speed * time
However, speed is given in km/h and time in seconds. To use the formula correctly, we must convert the speed to metres per second (m/s) and time to seconds. The standard conversion is:
1 km/h = 5 / 18 m/s
Step-by-Step Solution:
Step 1: Convert 1260 km/h to m/s.
Speed (m/s) = 1260 * (5 / 18).
First compute 1260 / 18 = 70.
Then multiply by 5: 70 * 5 = 350 m/s.
So the spaceship travels 350 metres every second.
Step 2: Convert the time interval to seconds.
One tenth of a second = 1 / 10 second = 0.1 second.
Step 3: Compute the distance covered in 0.1 second.
distance = speed * time = 350 * 0.1 metres.
350 * 0.1 = 35 metres.
Therefore, the spaceship travels 35 m in one tenth of a second.
Verification / Alternative check:
We can cross-check by first finding the distance traveled in one hour and then scaling down. In one hour, the spaceship covers 1260 km, which is 1260 * 1000 = 1,260,000 metres. One hour is 3600 seconds. So in one second, distance = 1,260,000 / 3600 metres, which equals 350 metres per second. In 0.1 second, it will cover 350 / 10 = 35 metres. This matches our earlier calculation.
Why Other Options Are Wrong:
126 m would require the spaceship to travel at 1260 m/s or a much higher km/h value, which does not match the given speed.
36 m is very close but comes from rounding 35 to the nearest whole number incorrectly when an exact calculation is possible.
42 m or 25 m correspond to other arbitrary speeds and do not result from the correct unit conversion of 1260 km/h to m/s.
Only 35 m is consistent with 1260 km/h over 0.1 second.
Common Pitfalls:
Learners often forget to convert km/h to m/s and directly multiply 1260 by 0.1, which mixes units incorrectly. Another common mistake is to use the wrong conversion factor, such as 18 / 5 rather than 5 / 18, leading to an incorrect speed in m/s. Careless arithmetic with decimals can also create small but significant errors. Keeping track of units at every step is the best way to avoid these pitfalls.
Final Answer:
The spaceship travels
35 m in one-tenth of a second at a speed of 1260 km/h.
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