25. At the end of a race, a runner decelerates from a velocity of $9.00 \mathrm{~m} / \mathrm{s}$ at a rate of $2.00 \mathrm{~m} / \mathrm{s}^{2}$. (a) How far does she travel in the next $5.00 \mathrm{~s}$ ? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?
Answer
Check: \(v_{f} > 0\) and \(d > 0\), so the results make sense.
Step 1 ：\(v_{0} = 9.00 \mathrm{~m} / \mathrm{s}\)
Step 2 ：\(a = -2.00 \mathrm{~m} / \mathrm{s}^{2}\)
Step 3 ：\(t = 5.00 \mathrm{~s}\)
Step 4 ：\(v_{f} = v_{0} + at = 9.00 - 2.00 \times 5.00 = \boxed{1.00} \mathrm{~m} / \mathrm{s}\)
Step 5 ：\(d = v_{0}t + \frac{1}{2}at^{2} = 9.00 \times 5.00 + \frac{1}{2}(-2.00)(5.00)^{2} = \boxed{22.50} \mathrm{~m}\)
Step 6 ：Check: \(v_{f} > 0\) and \(d > 0\), so the results make sense.
