A Thomson's gazelle can run at very high speeds, but its acceleration is relatively modest. A reasonable model for the sprint of a gazelle assumes an acceleration of \(4.2 \mathrm{~m} / \mathrm{s}^{2}\) for \(6.5 \mathrm{~s}\), after which the gazelle continues at a steady speed.

a. What is the gazelle's top speed?

b. A human would win a very short race with a gazelle. The best time for a \(30 \mathrm{~m}\) sprint for a human runner is \(3.6 \mathrm{~s}\). How much time would the gazelle take for a \(30 \mathrm{~m}\) race?

c. A gazelle would win a longer race. The best time for a \(200 \mathrm{~m}\) sprint for a human runner is \(19.3 \mathrm{~s}\). How much time would the gazelle take for a \(200 \mathrm{~m}\) race?