The maximal running speed of a mammal on the Serengeti could mean the difference between life and death. The maximal running speed of mammals is often considered as a function of their mass. The mass of adult big cats on the Serengeti vary from ? 40 kg for a leopard and ? 140 kg for a hunting lioness. Both of these predators can maintain a maximum speed of 60 km h ?1 . With a maximum speed of 110 km h ?1 and an average mass of 75 kg, the cheetah is the fastest land mammal on the Serengeti. There are also other predators on the Serengeti, the Hyena can also reach speeds of 50 km h ?1 with an adult mass of ? 45 kg [4]. Herbivores on the Serengeti can be both much smaller and much larger than their carnivorous counterparts with masses ranging from ? 20 kg for the Thomson's gazelle, to ? 400 kg for a plains zebra and ? 500 kg for the massive African buffalo. As you would imagine, the top speed of the gazelle is higher than that of the Buffalo, with speeds of 65 km h ?1 and 50 km h ?1 respectively. Zebras can reach a top speed of 65 km h ?1 . The most likely animal to be able to escape the clutches of the predators is the wildebeest with a weight of 250 kg and a top speed of 80 km h ?1 [4, 2]. Using this information, biologists have developed power law models for maximal running speed as a function of mass in mammals. However, in a study of the maximal running speeds of 106 different mammals, the authors of [4] concluded: "For all mammals (n=106) ... an equation of the form log10(MRS) = 1.47832 + 0.25892(log10(M)) ? 0.06237(log10(M))2 , yields a significantly better fit to the data. In the above, M is the mass of the mammal (in kg), and MRS is its maximal running speed (in kmh ?1 )

Neither predators nor prey can reach their top speed instantaneously, nor can they keep up their top speed indefinitely. In [3], it was found that the time taken for an animal to reach its top speed is dependent on its mass and that the model that best fits this relation is a power law of the form: tT S = aMb , where tT S is the time (in s) it takes the animal to reach top speed (or maximal running speed). To find the values of a and b the following data has been provided:

log10 M log10 ITS 1.48 0.16 1.78 0.41 2.08 0.67 2.38 0.93 2.68 1.18 Table 1: Acceleration data for mammals