The cheetah's maximum speed

Question

Another day on the Serengeti. A cheetah at rest spies her prey, a Thomson’s gazelle, and initiates a chase. The cheetah moves in a straight line, accelerating uniformly for the first 1.99 seconds of her motion and then continuing at her maximum speed for an additional 7.85 seconds before abandoning the chase. (Cheetahs are fast… but gazelles are fast too!) The cheetah ran a total distance of 250 meters during the chase. Find:

  (a) the cheetah's acceleration during the first part of her motion;

  (b) the cheetah’s maximum speed.

Equation:

0= v1+ at

X2= v1t + 1/2 at^2

Answer 1

250 = 1/2 a *1.99^2 + (a*1.99) * 7.85

Total distance = distance of the accelerated portion + distance of the constant speed portion

= v1 t1 + 1/2 a t1^2 + v2 t2

where v1 = 0, v2 = v1 + at = at

top speed = v2 = a t