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 6.5 s, after which the gazelle continues 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 19.3s.
How much time would the gazelle take for a 200 m race?

Answer 1

a) 27.3 m/s

b) 3.78 s

c) 10.576 s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

a)

`v=u+at\\\Rightarrow v=0+4.2* 6.5\\\Rightarrow v=27.3\ m/s`

Top speed of the gazelle is 27.3 m/s

b)

`s=ut+(1)/(2)at^2\\\Rightarrow 30=0t+(1)/(2)* 4.2* t^2\\\Rightarrow t=\sqrt{(30* 2)/(4.2)}\\\Rightarrow t=3.78\ s`

The gazelle would take 3.78 seconds to win a 30 m race.

c)

`s=ut+(1)/(2)at^2\\\Rightarrow s=0* 6.5+(1)/(2)* 4.2* 6.5^2\\\Rightarrow s=88.725\ m`

The gazelle would go 88.725 m with the acceleration after which there will be no acceleration.

Time = Distance / Speed

`\text{Time}=(200-88.725)/(27.3)=4.076\ s`

Total time taken by the gazelle to cover 200 m would be 6.5+4.076 = 10.576 seconds