Final answer:
The graph of speed vs. time represents how the speed of an object changes over time. If the object is moving to the east, the best description for the graph is that the speed is constant and velocity is changing.
Step-by-step explanation:
The graph of speed vs. time represents how the speed of an object changes over time. If the graph is showing a constant speed, it means that the object is moving at the same rate throughout the entire time period. On the other hand, if the graph is showing a changing speed, it means that the object is accelerating or decelerating.
Velocity, on the other hand, takes into account the direction of motion. If the object is moving to the east, it means that its velocity is positive, and if it is moving to the west, its velocity is negative. So, in the case of the graph showing a constant speed, the velocity would change from positive to zero if the object stops, and then it would change from zero to negative if the object starts moving in the opposite direction.
Therefore, the best description for the graph of speed vs. time when the object is moving to the east is: 'The speed is constant and velocity is changing.'