A Thomson\'s gazelle can run at very high speeds, but its acceleration is relati

Question

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/s^2 for 6.5s , after which the gazelle continues at a steady speed. What is the gazelle's top speed?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? 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?

Explanation / Answer

4.2 * 6.5= 27.3 m/s

D= 1/2at^2

30= 1/2 4.2* t^2

t= 3.78 s

D=1/2at^2

D= 1/2 *4.2 *6.5^2

D=88.725

D= vt

(200-88.725)= 27.3t

t= 4.08s

4.08+6.5= 10.58 s

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