Answer :
When the speed of a car is reduced by 12.9 percent, the braking distance decreases by approximately 26.9 percent.
To calculate the percentage decrease in braking distance, we can use the concept of proportionality. Braking distance is directly proportional to the square of the initial speed of the car. Therefore, if the speed is reduced by a certain percentage, the braking distance will decrease by a larger percentage.
Let's assume the initial braking distance is D. When the speed is reduced by 12.9 percent, the new speed becomes 100 percent minus 12.9 percent, which is 87.1 percent of the initial speed. Since the braking distance is directly proportional to the square of the speed, the new braking distance will be (87.1 percent)² of the initial braking distance.
The percentage decrease in braking distance can be calculated as follows:
Percentage decrease = (1 - New distance / Initial distance) * 100
Percentage decrease = (1 - (87.1 percent)²) * 100
Percentage decrease ≈ 1 - 0.7581 ≈ 0.2419 ≈ 24.19 percent
Therefore, the braking distance of the car decreases by approximately 24.19 percent when the speed of the car is reduced by 12.9 percent.
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