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:The correct answer will be:

(a)27.3 m/s(b)3.8 sExplanation: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]