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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 gazelles 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?

Answer :

Cricetus

Answer:

The correct answer will be:

(a) 27.3 m/s

(b) 3.8 s

Explanation:

According to the question:

Acceleration,

[tex]a= 4.2 \ m/s^2[/tex]

Time,

[tex]t = 6.5 \ s[/tex]

(a)

The gazelles top speed will be:

⇒  [tex]V_{max} = at[/tex]

             [tex]=4.2\times 6.5[/tex]

             [tex]=27.3 \ m/s[/tex]

or,

             [tex]= 27 \ m/s[/tex]

(b)

As we know,

s = 30 m

Now,

⇒  [tex]s = \frac{1}{2} at^2[/tex]

or,

⇒  [tex]t=\sqrt{\frac{2s}{a} }[/tex]

On putting the given values, we get

       [tex]=\sqrt{\frac{2\times 30}{4.2} }[/tex]

       [tex]=\sqrt{\frac{60}{4.2} }[/tex]

       [tex]=3.78 \ s[/tex]

or,

       [tex]=3.8 \ s[/tex]

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