(a)
The work-energy theorem states that the work done on the cheetah is equal to its change in kinetic energy:
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
(b) 6.1 cal
The conversion between calories and Joules is
1 cal = 4186 J
Here the energy the cheetah needs is
Therefore we can set up a simple proportion
to find the equivalent energy in calories: