Final answer:
To describe the motion in a free body diagram, one must consider the direction of both the velocity and acceleration vectors. If these vectors are in opposite directions, the object is slowing down. The details provided in the question indicate that without the diagram, the object could be either 'moving to the left and slowing down' or 'moving to the right and slowing down'.
Step-by-step explanation:
To accurately describe the motion depicted by the free body diagram, we need to understand the relationship between velocity and acceleration. When the velocity vector is positive (to the right) and the acceleration vector is negative (to the left), the object is slowing down. Conversely, if the velocity vector is negative (to the left) and the acceleration vector is positive (to the right), the object is also slowing down. Part a of Figure 3.3 depicts this, with the velocity and acceleration vectors acting in opposite directions, indicating deceleration. Hence, the correct statement that describes the motion would be either: 'The object is moving to the left and slowing down.' if the velocity is negative, or 'The object is moving to the right and slowing down.' if the velocity is positive.
If we consider Figure 2.14 (c) and (d), they further illustrate the concepts where (c) shows an object moving to the left and slowing down, with a positive acceleration in our coordinate system, and (d) shows an object moving to the left and speeding up with negative acceleration. Therefore, without knowing the exact direction of the velocity vector from the student's description, both options b and d from the initial question's choices could be correct, based on the information given about deceleration and direction of motion.
Lastly, the position vs time graph of an object that is speeding up is not a straight line - this is a false statement. A straight line on a position vs time graph would represent an object moving at a constant speed, not one that's speeding up. Therefore, if the object is accelerating, we would expect a curved line on the graph.