Final answer:
The cheetah's average speed during the chase is 28.9 m/s, and its displacement is approximately 55.9m, leading to an average velocity of 20.7 m/s towards the northwest.
Step-by-step explanation:
Cheetahs are the fastest land animals, capable of reaching high speeds. When a cheetah chases an impala, it can exhibit significant changes in speed and direction, which are aspects of displacement and velocity in physics. In the given scenario, a cheetah's average speed and average velocity can be calculated based on the displacement over time.
Average Speed
Average speed is calculated as the total distance divided by the total time. The cheetah covers 32m north and then 46m west, which adds up to a total distance of 32m + 46m = 78m. As the motion took 2.7 seconds, the average speed is 78m / 2.7s = 28.9 m/s.
Average Velocity
Average velocity is a vector quantity and is calculated using the displacement from the starting point to the ending point. The displacement can be found using the Pythagorean theorem with the north and west movements as perpendicular components. The displacement is the square root of (32m)2 + (46m)2 which is approximately 55.9m. Thus, the average velocity magnitude is 55.9m / 2.7s = 20.7 m/s. The direction of this velocity vector is towards the northwest, but the exact angle can be calculated using trigonometry if needed.