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

The correct answer will be:

(a) 27.3 m/s

(b) 3.8 s

Step-by-step 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* 6.5`

`=27.3 \ m/s`

or,

`= 27 \ m/s`

(b)

As we know,

s = 30 m

Now,

⇒
`s = (1)/(2) at^2`

or,

⇒
`t=\sqrt{(2s)/(a) }`

On putting the given values, we get

`=\sqrt{(2* 30)/(4.2) }`

`=\sqrt{(60)/(4.2) }`

`=3.78 \ s`

or,

`=3.8 \ s`