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Solve the all parts of given problem:

Problem: 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 4.2m/s² for 6.5s, after which the gazelle continues at a steady speed.

Part I: What is the gazelle's top speed?

Part II: A human would win a very short race with a gazelle. The best time for a 30 m sprint for a human runner is 3.6 s. How much time would the gazelle take for a 30 m race?

Part III: A gazelle would win a longer race. The best time for a 200 m sprint for a human runner is 19.3 s. How much time would the gazelle take for a 200 m race?

Please include each step and the equations you used. Thanks!

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