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The cheetah and the pronghorn

 The pronghorn antelope in the Western Great Plains of the US is one of the fastest animals on the planet. But it has outlived all its predators and now runs where none pursues. Let’s imagine a cheetah-like predator in the period tens of thousands of years ago when the pronghorn evolved its speed. A cheetah is one of the fastest animals, but it can only maintain its high speed for a short time. The pronghorn can continue to run at a steady pace of 80 km/hr for a long time. Here are some of the parameters of the cheetah’s motion. Max speed 120 km/hr Can accelerate from 0 to 120 km/hr in 3 seconds Can maintain max speed (sprint) for about 30 seconds. After its initial high-speed sprint, it quickly drops to a steady pace of ~70 km/hr.

A. During the time it is accelerating, what is the cheetah’s average acceleration, <a>, and its average speed, <v>?

B. Suppose the cheetah comes across a herd of antelope running at a steady pace of 80 km/hr. As soon as they see the cheetah, they wheel and run directly away from the cheetah. How far from the cheetah do the pronghorns have to be if they are to be safe? Explain your reasoning.