Question

the force of the airs resistance to a certain car (in newtons) as a function of the cars speed (in km/h) is graphed.
what is the approximate average rate at which the airs resistance increases, as the car accelerates from 50 km/h to 65 km/h?
choose 1 answer:
8 n per km/h
9\frac{1}{3} n per km/h
11\frac{2}{3} n per km/h
14 n per km/h
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Explanation:

Step1: Find the resistance at \(50\) km/h and \(65\) km/h

From the graph, when \(x = 50\) km/h, \(y\approx200\) N; when \(x = 65\) km/h, \(y\approx410\) N.

Step2: Use the average - rate - of - change formula

The average rate of change formula is \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 50\), \(y_1=200\), \(x_2 = 65\), \(y_2 = 410\).
\(\frac{y_2 - y_1}{x_2 - x_1}=\frac{410 - 200}{65 - 50}=\frac{210}{15}\)

Step3: Calculate the value

\(\frac{210}{15}=14\)

Answer:

\(14\) N per km/h (Option D)