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
Equation: d = 0.05r^2 + r
1. What does the equation d = 0.05r^2 + r represent?
The equation represents the distance, d, in feet traveled by a car moving at a speed of r miles per hour (r is the speed of the car) after the driver begins to stop the car.
2. What is the significance of the term 0.05r^2 in the equation?
The term 0.05r^2 represents the distance, in feet, covered by the car due to skid marks.
3. What is the significance of the term r in the equation?
The term r represents the distance, in feet, covered by the car due to the initial momentum before the brakes are applied.
4. How can the formula be used to determine the speed of the car when the skid mark distance is zero?
If the skid mark distance is zero, it means the car stopped instantly. In this case, the formula can be set to d = 0 and solved for r, giving us the speed of the car at the point of applying the brakes.
To answer the questions related to the given situation, we can use the equation provided:
d = 0.05r^2 + r
where:
- d represents the distance traveled by the car in feet,
- r represents the speed of the car in miles per hour.
Now, let's proceed to answer the questions based on this equation.