Answer :
Final answer:
In this question, we use equations of motion to calculate that it would take approximately 5 seconds for a cheetah, accelerating at 4 m/s² from rest, to catch a gazelle running at a constant velocity of 10 m/s, if the gazelle had a 59.1 m head start. This result assumes the cheetah can instantly reach top speed.
Explanation:
The problem requires us to solve for time using the concepts of velocity and acceleration. To find the time it takes the cheetah to catch the gazelle, we can use the cheetah's acceleration and the gazelle's constant velocity, given as 10 m/s, which is the average velocity since the gazelle is not accelerating. In the first stage, both animals are running at their top speeds, with the cheetah at 102 km/h and the gazelle at 73.4 km/h.
The gazelle is 59.1 meters ahead. In the second stage, we need to calculate the time when the cheetah will reach the gazelle. The acceleration of the cheetah is given as 4 m/s². Using this data, the calculated time for the cheetah to reach the gazelle is 20 divided by 2(10 m/s) times 4 m/s² which results in approximately 5 seconds. However, this calculation assumes the cheetah can instantly reach top speed, which is not biologically accurate.
Learn more about Motion equations here:
https://brainly.com/question/35709307
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