Question

4.4 the mean value theorem: problem 6
(6 points)
results for this submission
the answer is not correct.
at 2:00pm a cars speedometer reads 50mph, and at 2:10pm it reads 70mph. use the mean value theorem to find an acceleration the car must achieve.
answer( in mi/h²):

Explanation:

Step1: Convert time interval

The time interval from 2:00 pm to 2:10 pm is \(t = 10\) minutes. Since \(1\) hour \(= 60\) minutes, \(t=\frac{10}{60}=\frac{1}{6}\) hours.

Step2: Apply the Mean - Value Theorem

Let \(v(t)\) be the velocity function of the car. By the Mean - Value Theorem, if \(v(t)\) is continuous on the closed interval \([a,b]\) and differentiable on the open interval \((a,b)\), then \(v^{\prime}(c)=\frac{v(b)-v(a)}{b - a}\). Here, \(a\) is the start - time (\(t = 0\) hours, \(v(a)=50\) mph), \(b=\frac{1}{6}\) hours (\(v(b) = 70\) mph), and \(v^{\prime}(t)\) is the acceleration \(a(t)\).

$$a(c)=\frac{v(b)-v(a)}{b - a}=\frac{70 - 50}{\frac{1}{6}-0}$$

$$a(c)=\frac{20}{\frac{1}{6}}=120$$

Answer:

\(120\)