(a) [tex]2.56\cdot 10^4 J[/tex]
The work-energy theorem states that the work done on the cheetah is equal to its change in kinetic energy:
[tex]W= \Delta K = \frac{1}{2}mv^2 - \frac{1}{2}mu^2[/tex]
where
m = 51.0 kg is the mass of the cheetah
u = 0 is the initial speed of the cheetah (zero because it starts from rest)
u = 31.7 m/s is the final speed
Substituting, we find
[tex]W=\frac{1}{2}(51.0 kg)(31.7 m/s)^2 - \frac{1}{2}(51.0 kg)(0)^2=2.56\cdot 10^4 J[/tex]
(b) 6.1 cal
The conversion between calories and Joules is
1 cal = 4186 J
Here the energy the cheetah needs is
[tex]E=2.56\cdot 10^4 J[/tex]
Therefore we can set up a simple proportion
[tex]1 cal : 4186 J = x : 2.56\cdot 10^4 J[/tex]
to find the equivalent energy in calories:
[tex]x=\frac{(1 cal)(2.56\cdot 10^4 J)}{4186 J}=6.1 cal[/tex]
