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/s2 for 6.5s , 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 m sprint for a human runner is 3.6 s. How much time would the gazelle take for a 30 m race?

c.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

a) find the velocity with velocity = acceleration * time = 27.3 m/s
b) rearange x=(1/2)at^2+Vo*t to find t, x=distance, a=acceleration, t=time, Vo=original velocity (Vo=0 so its really just rearanging x=(1/2)a t^2 to find t)
30 = 0.5 *4.2* t^2
t = 3.78 s

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