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

Sure! Let's break down the given information and the equation provided:

Given:
- Distance traveled by the car after the driver begins to stop is denoted by "d."
- Speed of the car (in miles per hour) at the time the driver applied the brakes is denoted by "r."
- The formula for calculating the distance traveled is d = 0.05r^2 + r.

Now, let's answer the four questions based on this situation:

Question 1: What does the variable "r" represent in the equation d = 0.05r^2 + r?
Answer: In the equation, "r" represents the speed of the car at the time the driver applied the brakes.

Question 2: What does the variable "d" represent in the equation d = 0.05r^2 + r?
Answer: In the equation, "d" represents the distance traveled by the car after the driver begins to stop.

Question 3: How does the equation d = 0.05r^2 + r model the situation?
Answer: The equation models the situation by using the speed of the car (r) to calculate the distance traveled (d) after the driver begins to stop. It incorporates the relationship between speed and stopping distance, where the faster the car is initially moving, the longer the distance it will travel before coming to a stop.

Question 4: What would a distance of zero (d = 0) in the equation d = 0.05r^2 + r indicate?
Answer: If the distance (d) in the equation is zero, it means that the car was able to stop instantly. In other words, if the distance traveled after applying the brakes is zero, it indicates that the car came to a complete stop without any skid marks.