The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 45.7 cm and a mass of 9.1kg. How many revolutions did one of the front tires (assuming only the back tires spun upon starting), make as the car covered the distance?
To find the number of revolutions made by one of the front tires as the car covers the distance, we need to determine the distance covered by one revolution of the tire and then calculate the number of revolutions.
1. Calculate the circumference of the tire:
Circumference = π * diameter
Given that the diameter of the tire is 45.7 cm, the circumference can be calculated as follows:
Circumference = 3.14 * 45.7 cm
Therefore, the circumference of the tire is 143.078 cm.
2. Calculate the total distance covered by the car in miles:
In the question, it is mentioned that the car covers 0.25 miles in 15 seconds. To find the distance covered by the car in one second, divide the total distance by the time taken:
Distance covered in one second = 0.25 miles / 15 seconds
Therefore, the car covers approximately 0.0167 miles in one second.
3. Find the number of seconds required for one revolution of the tire:
To calculate this, divide the time taken by the car to cover the distance by the number of revolutions of the tire:
Time for one revolution = 15 seconds / (Total number of revolutions of the tire)
We want to find the number of revolutions, so we rewrite the equation as follows:
Total number of revolutions of the tire = 15 seconds / (Time for one revolution)
4. Convert the distance covered by the car in miles to centimeters:
Since we know the circumference of the tire in centimeters, it will be easier to work with consistent units. Therefore, we need to convert the distance covered by the car to centimeters:
Distance covered by the car = 0.25 miles * 1609.34 meters/mile * 100 centimeters/meter
By performing the calculations, the distance covered by the car is approximately 40,233.5 cm.
5. Calculate the total number of revolutions made by the tire:
By dividing the distance covered by the car by the circumference of the tire, we can find the number of revolutions made by one of the front tires:
Total number of revolutions of the tire = Distance covered by the car / Circumference
Plugging in the values, we get:
Total number of revolutions of the tire = 40,233.5 cm / 143.078 cm
By performing the calculations, we find that the total number of revolutions made by the tire is approximately 281.137.
Therefore, one of the front tires made approximately 281.137 revolutions as the car covered the given distance.