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show all you work, including units, on separate paper. follow the \problem solving method\.
this final exam is cumulative and covers material from the entire course.
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from the list of choices, select the one best answer.
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question 10 of 62
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a dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. what is its velocity when it crosses the finish line? 1 hr = 3,600 s
135 mi/h
269 mi/h
188 mi/h
296 mi/h

Explanation:

Step1: Recall kinematic equation for constant acceleration

For an object starting from rest (\(u = 0\)), the displacement \(s\) is given by \(s=\frac{1}{2}at^{2}\), and the final velocity \(v\) is given by \(v = u+at=at\) (since \(u = 0\)). Also, we can relate \(s\) and \(v\) using the equation \(v^{2}=u^{2}+2as\), and since \(u = 0\), this simplifies to \(v^{2}=2as\). First, we need to find the acceleration \(a\) from the displacement and time, then find the final velocity.

The displacement \(s=\frac{1}{4}\text{ mi}\), time \(t = 6.70\text{ s}\), initial velocity \(u = 0\).

From \(s=\frac{1}{2}at^{2}\), we can solve for \(a\): \(a=\frac{2s}{t^{2}}\)

Substitute \(s=\frac{1}{4}\text{ mi}\) and \(t = 6.70\text{ s}\):

\(a=\frac{2\times\frac{1}{4}\text{ mi}}{(6.70\text{ s})^{2}}=\frac{0.5\text{ mi}}{44.89\text{ s}^{2}}\approx0.01114\text{ mi/s}^{2}\)

Step2: Find final velocity \(v\)

Using \(v = at\) (since \(u = 0\)):

\(v=0.01114\text{ mi/s}^{2}\times6.70\text{ s}\approx0.0746\text{ mi/s}\)

Now, convert this velocity from mi/s to mi/h. We know that \(1\text{ h}=3600\text{ s}\), so to convert from mi/s to mi/h, we multiply by 3600:

\(v = 0.0746\text{ mi/s}\times3600\text{ s/h}\approx268.56\text{ mi/h}\approx269\text{ mi/h}\)

Alternatively, we can use the equation \(s=\frac{u + v}{2}t\) (since for constant acceleration, average velocity \(\bar{v}=\frac{u + v}{2}\) and \(s=\bar{v}t\)). Since \(u = 0\), this becomes \(s=\frac{v}{2}t\), so \(v=\frac{2s}{t}\)

Substitute \(s=\frac{1}{4}\text{ mi}\) and \(t = 6.70\text{ s}\):

\(v=\frac{2\times\frac{1}{4}\text{ mi}}{6.70\text{ s}}=\frac{0.5\text{ mi}}{6.70\text{ s}}\approx0.0746\text{ mi/s}\)

Convert to mi/h: \(0.0746\text{ mi/s}\times3600\text{ s/h}\approx268.56\text{ mi/h}\approx269\text{ mi/h}\)

Answer:

269 mi/h (Option: 269 mi/h)