Use the following situation to answer the next four questions. The formula for these questions came from the police department. They use this formula to determine the speed at which the car was going when the driver applied the brakes, by measuring the distance of the skid marks. So when you get to problem 16, it is referring to what a person would interpret the situation if the skid mark was zero distance. So, if the skid mark distance equaled zero, that would mean, the speed of the vehicle, r, was zero, or that the car was able to stop instantly. For these questions, the equation d = 0.05r2 + r models the distance, d, in feet traveled by a car moving r miles per hour (r is the speed of the car) after the driver begins to stop the car

Question

Use the following situation to answer the next four questions. The formula for these questions came from the police department. They use this formula to determine the speed at which the car was going when the driver applied the brakes, by measuring the distance of the skid marks. So when you get to problem 16, it is referring to what a person would interpret the situation if the skid mark was zero distance. So, if the skid mark distance equaled zero, that would mean, the speed of the vehicle, r, was zero, or that the car was able to stop instantly. For these questions, the equation d = 0.05r2 + r models the distance, d, in feet traveled by a car moving r miles per hour (r is the speed of the car) after the driver begins to stop the car

Answer 1

Alright, let's get started with the questions.

Question 1: What does the formula d = 0.05r^2 + r represent?
Answer: The formula represents the distance, d, in feet traveled by a car when the driver applies the brakes after the car is moving at a speed of r miles per hour. The distance traveled is a function of the speed of the car.

Question 2: How is the speed of the car, r, related to the distance traveled, d?
Answer: The speed of the car, r, is a variable in the formula that determines the distance traveled, d. As the speed of the car increases, the distance traveled also increases.

Question 3: What does it mean when the skid mark distance is zero?
Answer: When the skid mark distance is zero, it means that the car was able to stop instantly. In the context of the formula, if the skid mark distance is zero, it indicates that the speed of the car, r, was also zero.

Question 4: If the formula is used to calculate the distance traveled, can it be used in reverse to determine the initial speed of the car before braking?
Answer: Yes, the formula can be rearranged to solve for the initial speed of the car before braking. By rearranging the formula, we can find the value of r (the speed of the car) when a given distance, d, is known. This can be useful in forensic analysis or accident reconstruction to determine the initial speed of the car based on the skid mark distance.