Use the functions to find the stopping distance on wet pavement and dry pavement for a car traveling at 55 MPH.Identify the graph for each stopping distance.Explain how well your answers to item 1 model the actual stopping distances shown in Figure 3.41 on Page 384.Determine speeds on wet pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Explain how this is shown on the graphs
To find the stopping distance on wet and dry pavements, we can use the appropriate stopping distance functions. Let's start by calculating the stopping distance on dry pavement.
The stopping distance on dry pavement can be determined using the equation:
Stopping Distance (dry) = (Initial Velocity * Reaction Time) + (Initial Velocity^2 / (2 * Coefficient of Friction * Acceleration due to Gravity))
Given that the initial velocity is 55 MPH, we need to convert it to feet per second (fps). To do so, we multiply it by 1.47 (as 1 mile = 5280 feet, and 1 hour = 3600 seconds).
So, initial velocity in fps = 55 * 1.47 = 80.85 fps.
Next, we need to find the coefficient of friction for dry pavement. According to Figure 3.41 on Page 384, the coefficient of friction for dry pavement is approximately 0.7.
The reaction time is typically around 1 second.
We can now calculate the stopping distance on dry pavement using the formula:
Stopping Distance (dry) = (80.85 * 1) + (80.85^2 / (2 * 0.7 * 32.2)).
Once calculated, the stopping distance on dry pavement is approximately equal to 235.67 feet.
Now, let's determine the stopping distance on wet pavement using the equation:
Stopping Distance (wet) = (Initial Velocity * Reaction Time) + (Initial Velocity^2 / (2 * Coefficient of Friction * Acceleration due to Gravity))
The coefficient of friction for wet pavement is different from that of dry pavement. According to Figure 3.41 on Page 384, the coefficient of friction for wet pavement is approximately 0.4.
Using the same initial velocity of 55 MPH, converted to fps as 80.85 fps, and a reaction time of 1 second, we can calculate the stopping distance on wet pavement as follows:
Stopping Distance (wet) = (80.85 * 1) + (80.85^2 / (2 * 0.4 * 32.2)).
After the calculation, the stopping distance on wet pavement is approximately equal to 270.42 feet.
Now, let's identify the graphs for each stopping distance. Generally, stopping distance is related to the initial velocity of the car. As the velocity increases, the stopping distance also increases. That means the graph for stopping distance will be an upward sloping curve. However, we need to consider different coefficients of friction for wet and dry pavements.
For the stopping distance on dry pavement, the graph would be represented by a curve with a relatively smaller slope compared to wet pavement due to a higher coefficient of friction. The graph would show increasing stopping distances as the initial velocity increases.
For the stopping distance on wet pavement, the graph would be represented by a curve with a steeper slope due to a lower coefficient of friction. The graph would show greater increases in stopping distance as the initial velocity increases.
As for how well our answers model the actual stopping distances shown in Figure 3.41 on Page 384, we can evaluate the accuracy by comparing the calculated stopping distances to the values presented in the figure. If our calculated stopping distances are close to the values on the graph, then our answers can be considered as good estimators of the actual stopping distances. However, without the specific numbers from Figure 3.41, it is not possible to determine the exact accuracy of our answers.
To determine the speeds on wet pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet, we need to analyze the graphs.
First, we identify the point on the graph where the stopping distance exceeds 540 feet. This will give us the corresponding initial velocity. Using this velocity, we can then convert it back to MPH to provide the answer.
Keep in mind that the specific values and graph positioning may vary depending on the friction coefficient and other factors, but the general concept applies.
By looking at the graph for stopping distance on wet pavement, we can trace the curve until we reach the spot where the stopping distance exceeds 540 feet. This will give us the corresponding initial velocity.
To summarize, by analyzing the equation and graphs, we can determine the stopping distance on wet and dry pavements for a car traveling at 55 MPH. We can also identify the corresponding graphs for each stopping distance. Additionally, by examining the graphs further, we can determine the speeds on wet pavement that require stopping distances exceeding 540 feet.
To find the stopping distance on wet pavement and dry pavement, we can use a mathematical model called the stopping distance formula. Let's denote the stopping distance as D, the initial speed as v, and the coefficient of friction between the tires and the road as μ.
1. Stopping distance on dry pavement:
The stopping distance on dry pavement can be calculated using the formula:
D(dry) = (v^2) / (2 * g * μ(dry))
where g is the acceleration due to gravity (approximately 32.2 ft/s^2 in the US).
2. Stopping distance on wet pavement:
The stopping distance on wet pavement can be calculated using the formula:
D(wet) = (v^2) / (2 * g * μ(wet))
To determine the graph for each stopping distance, we need values for the coefficient of friction on dry and wet pavement. Unfortunately, this information is not provided, so we are unable to identify the specific graphs.
Regarding the actual stopping distances shown in Figure 3.41 on Page 384, we cannot comment on how well our calculations model these stopping distances without knowing the values of μ(dry) and μ(wet) used in the graph. The graph likely presents experimentally obtained or calculated stopping distances for different speeds and road conditions.
To find the speeds on wet pavement requiring stopping distances exceeding the length of 540 feet (one and one-half football fields), we can use the stopping distance formula. We need to find the speed at which D(wet) is greater than 540 feet.
D(wet) > 540 ft
(v^2) / (2 * g * μ(wet)) > 540 ft
From this inequality, we can solve for the speed (v) required for a stopping distance exceeding 540 feet on wet pavement.
Keep in mind that without the actual values of μ(wet), we cannot provide an accurate numerical solution or determine how this would be shown on the graphs.