Ketan made five rounds of a square park whose one side is 150 m, on a bicycle. He took 30 minutes for it. What was the speed of the bicycle?
Understand the Problem
The question is asking us to calculate the speed of a bicycle based on the distance Ketan traveled and the time taken. To find the speed, we will first determine the total distance covered, which is the perimeter of the square park multiplied by the number of rounds. Then, we will divide that distance by the time taken to find the speed in meters per minute or meters per second.
Answer
The speed of the bicycle is given by $ v = \frac{4Ln}{T} $, where $ L $ is the side length of the park in meters, $ n $ is the number of rounds, and $ T $ is the time taken in seconds.
Answer for screen readers
The speed of the bicycle is given by the formula:
$$ v = \frac{4Ln}{T} $$
where ( L ) is the length of one side of the square park, ( n ) is the number of rounds, and ( T ) is the total time taken in seconds.
Steps to Solve
- Calculate the perimeter of the square park
To find the perimeter of a square park, use the formula:
$$ P = 4s $$
where $s$ is the length of one side of the square.
Assume $s = L$ (the given length of the side).
- Determine total distance traveled
Multiply the perimeter by the number of rounds Ketan completed. If he completes $n$ rounds, the total distance $D$ will be calculated as:
$$ D = P \times n = (4L) \times n $$
- Convert time into appropriate units
Make sure the time taken $T$ (given in minutes or seconds) matches the units used for distance (meters). If the time is given in minutes and you want the speed in meters per second, convert minutes to seconds by multiplying by 60:
$$ T = T \text{ (in minutes)} \times 60 $$
- Calculate speed
Now, calculate speed $v$ using the formula:
$$ v = \frac{D}{T} $$
Substituting the values derived previously:
$$ v = \frac{D}{T} = \frac{(4L \times n)}{T} $$
This will give you the speed in meters per second.
The speed of the bicycle is given by the formula:
$$ v = \frac{4Ln}{T} $$
where ( L ) is the length of one side of the square park, ( n ) is the number of rounds, and ( T ) is the total time taken in seconds.
More Information
The formula for speed calculated here is based on the relationship between distance, time, and speed which is foundational in physics and is frequently used in real-life scenarios including travel and sports.
Tips
- Not converting time units properly: Ensure that time is in seconds if the speed is measured in meters per second.
- Forgetting to multiply by the number of rounds: Always include the number of rounds when calculating the total distance traveled.
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