predicting the stopping distance for a car traveling 45 miles per hour using this chart

speed stopping
(mph) Distance (FT)
55 273
56 355
75 447

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To predict the stopping distance for a car traveling at 45 miles per hour using the given chart, we can use a method called interpolation. Interpolation is the process of estimating values between two known data points.

In this case, we need to find the stopping distance for a speed of 45 miles per hour, which falls between the speeds listed in the chart.

To begin, let's identify the two speeds in the chart that are closest to 45 miles per hour. From the provided chart, we see that the closest speeds are 55 mph and 56 mph.

Next, we can find the corresponding stopping distances for these speeds. According to the chart, at 55 mph, the stopping distance is 273 ft, and at 56 mph, it is 355 ft.

Now, we can use the interpolation formula to estimate the stopping distance at 45 mph:

Stopping Distance at 45 mph = Stopping Distance at 55 mph + (Difference in Speeds) * (Stopping Distance at 56 mph - Stopping Distance at 55 mph)

Using the values we found, we can calculate the stopping distance:

Stopping Distance at 45 mph = 273 ft + (45 mph - 55 mph) * (355 ft - 273 ft)
Stopping Distance at 45 mph = 273 ft + (-10 mph) * (355 ft - 273 ft)

Simplifying the equation:

Stopping Distance at 45 mph = 273 ft + (-10 mph) * (82 ft)
Stopping Distance at 45 mph = 273 ft - 820 ft
Stopping Distance at 45 mph = -547 ft

Based on this calculation, the estimated stopping distance at 45 mph is -547 feet. However, it's important to note that this result is not a physically meaningful value since stopping distances cannot be negative. Hence, the interpolation method may not be appropriate in this case.

In order to accurately determine the stopping distance at 45 mph, we would need additional data points closer to this speed or a more accurate chart.