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1. 27.3 m/s
The velocity of the gazelle at any time is given by:
where
u is the initial velocity
a is the acceleration
t is the time
Here we have:
u = 0 (the gazelle starts from rest)
t = 6.5 s
Substituting the data, we find the gazelle's top speed:
2. 3.8 s
The distance covered by the gazelle is
d = 30 m
We know that the gazelle accelerates during the first part of the motion and then it continues at constant speed. We need to find first if the gazelle completes the race during the first part of its motion (accelerated motion); to do this, we can calculate what would be the distance covered by the gazelle before reaching the top speed, after t = 6.5 s:
Which is larger than 30 m: this means that the gazelle covers the 30 m during its accelerated motion. Therefore, we can use again the equation:
And substituting d = 30 m, we find the time:
3. 10.6 s
In this case, the distance the gazelle must cover is 200 m.
We know that in the first 6.5 s, the gazelle covers a distance of 88.7 m.
In the second part of the motion, the gazelle continues at its top speed, which is:
v = 27.3 m/s
The gazelle still have to cover a distance of
Therefore, the time taken to cover this distance is
So, the total time the gazelle needs to cover 200 m is
t = 6.5 + 4.1 = 10.6 s