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 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 1

Answer:

The correct answer will be:

(a) 27.3 m/s

(b) 3.8 s

Explanation:

According to the question:

Acceleration,

$a= 4.2 \ m/s^2$

Time,

$t = 6.5 \ s$

(a)

The gazelles top speed will be:

⇒  $V_{max} = at$

             $=4.2\times 6.5$

             $=27.3 \ m/s$

or,

             $= 27 \ m/s$

(b)

As we know,

s = 30 m

Now,

⇒  $s = \frac{1}{2} at^2$

or,

⇒  $t=\sqrt{\frac{2s}{a} }$

On putting the given values, we get

       $=\sqrt{\frac{2\times 30}{4.2} }$

       $=\sqrt{\frac{60}{4.2} }$

       $=3.78 \ s$

or,

       $=3.8 \ s$