What is the average speed of a cat whose position function is described by r + (1.2m/s)ti + (0.7m + (0.5m/s²)t²)j between t = 0.0s and t = 4.0s?

To find the average speed of the cat over the given time interval from (t = 0.0) seconds to (t = 4.0) seconds, we start by determining the displacement of the cat using the provided position function.

The position function given is ( r + (1.2 , \text{m/s})ti + (0.7,m + (0.5,\text{m/s}^2)t^2)j ). We can break this down:

1. The (x) component, from the term ((1.2, \text{m/s})ti), indicates linear motion at a constant speed of (1.2 , \text{m/s}).

2. The (y) component, from ((0.7,m + (0.5,\text{m/s}^2)t^2)j), shows that the cat's (y) position is influenced by both a constant displacement of (0.7,m) and a quadratic term (0.5,\text{m/s}^2 t^2), indicating that the cat accelerates in the (y