Answer
(a) KE = 35,800 J
(b) If the cheetah's speed were doubled, the kinetic energy of the cheetah would increase by a factor of 4.
Work Step by Step
(a) $KE = \frac{1}{2}mv^2$
$KE = \frac{1}{2}(70~kg)(32~m/s)^2$
$KE = 35,800~J$
(b) $KE_1 = \frac{1}{2}mv^2$
$KE_2 = \frac{1}{2}m(2v)^2 = 4\times \frac{1}{2}mv^2$
$KE_2 = 4\times KE_1$
Doubling the speed increases the kinetic energy by a factor of 4. We can verify this fact with the data for the cheetah.
$KE_2 = \frac{1}{2}(70~kg)(64~m/s)^2$
$KE_2 = 143,200~J$
If the cheetah's speed were doubled, the kinetic energy of the cheetah would increase by a factor of 4.
