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Multiple-Concept Example 13 presents useful background for this problem. The cheetah is one of the fastest accelerating animals, for it can go from rest to 30.4 m/s in 5.40 s. If its mass is 108 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower.

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Answer:

9241.6 W or 12.39318 hp

Explanation:

u = Initial velocity = 0

v = Final velocity

m = Mass

t = Time taken

Energy

[tex]KE=\frac{1}{2}m(v^2-u^2)\\\Rightarrow KE=\frac{1}{2}108(30.4^2-0^2)\\\Rightarrow KE=49904.64\ Joules[/tex]

Power

[tex]P=\frac{KE}{t}\\\Rightarrow P=\frac{49904.64}{5.4}\\\Rightarrow P=9241.6\ W[/tex]

Converting to hp

[tex]1\ W=\frac{1}{745.7}\ hp[/tex]

[tex]\\\Rightarrow 9241.6\ W=\frac{9241.6}{745.7}\ hp=12.39318\ hp[/tex]

The power developed by the cheetah is 9241.6 W or 12.39318 hp

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