The world's fastest mammal

The cheetah is the fastest mammal in the world, with a maximum accelerative ability of roughly 9 m/s${}^2$‍. Scientists have attributed this remarkable ability to the cheetah’s unique physical composition. Evolutionary specialization led to the species’ small, lithe build, which makes the cat aerodynamic. The cheetah’s respiratory and circulatory system are abnormally large to allow for quicker oxygen uptake. Finally, its exceptionally long, muscular tail acts as a counter-torque mechanism to maintain the cheetah’s balance and center of mass during high-speed chases. See Figure 1.

Figure 1. While chasing prey, the cheetah’s tail acts as a rudder and counters the body’s movement during sharp turns.

Scientists interested in further studying the physical properties of cheetahs travel to the African savannah. There, they observe a cheetah that is hiding in the tall brush. A gazelle runs right past the hiding cheetah. Immediately after the gazelle passes the cheetah, the cheetah starts to pursue the unsuspecting gazelle.

The velocity vs. time graphs for the animals in this scenario are given below. At time t=0 seconds the cheetah emerges from the brush.

Figure 2. The velocity vs time graph of both the cheetah and the gazelle.