Critical Thinking 5. Does knowing the distance between two objects give you enough infor- mation to locate the objects? Explain. Interpreting Graphics 6. Figure 1.9 shows position-time graphs of the straight-line movement of two brown bears in a wildlife preserve . Which bear has the greater aver age velocity over the entire period? Which bear has the greater velocity at t=8.0min ? Is the velocity of bear A always positive? Is the velocity of bear B ever negative?

Critical Thinking<br />5. Knowing the distance between two objects does not provide enough information to locate the objects. Distance only tells us how far apart the objects are, but it does not give us any information about their specific positions or directions. To accurately locate the objects, we would need additional information such as their coordinates, direction of movement, or any other relevant details that can help us determine their exact positions.<br /><br />Interpreting Graphics<br />6. To determine which bear has the greater average velocity over the entire period, we need to calculate the slope of the position-time graphs for both bears. The bear with the steeper slope will have the greater average velocity. <br /><br />To find the velocity at $t=8.0min$, we can look at the slopes of the tangent lines at that specific point on the graphs. The bear with the steeper tangent line slope at $t=8.0min$ will have the greater velocity at that time.<br /><br />To determine if the velocity of bear A is always positive, we can look at the direction of the slope of the position-time graph for bear A. If the slope is always increasing (going upwards), then the velocity of bear A is always positive. <br /><br />Similarly, to determine if the velocity of bear B is ever negative, we can look at the direction of the slope of the position-time graph for bear B. If the slope is ever decreasing (going downwards), then the velocity of bear B is ever negative.