FIGURE EX1.10 shows two dots of a motion diagram and vector . Copy this figure, then add dot 4 and the next velocity vector if the acceleration vector at dot 3 (b) points left.

Verified step by step guidance

1. Identify the given information: Dot 3 has a velocity vector \( \vec{v}_3 \) pointing to the right, and the acceleration vector at dot 3 points to the left.
2. Since the acceleration vector points to the left, it indicates that the object is decelerating as it moves to the right.
3. To add dot 4, we need to place it to the right of dot 3, but closer than the distance between dot 2 and dot 3, due to the deceleration.
4. Draw the new velocity vector \( \vec{v}_4 \) at dot 4. Since the object is decelerating, \( \vec{v}_4 \) should be shorter than \( \vec{v}_3 \) and still point to the right.
5. Ensure the acceleration vector at dot 3 is drawn pointing to the left, indicating the direction of deceleration.

Key Concepts

Motion Diagrams

Motion diagrams visually represent the position of an object at various time intervals. Each dot indicates the object's position at a specific moment, while arrows represent velocity vectors, showing the direction and magnitude of motion. Understanding these diagrams is crucial for analyzing how an object's position changes over time and how it relates to velocity and acceleration.

Velocity and Acceleration

Velocity is a vector quantity that describes the rate of change of an object's position, including both speed and direction. Acceleration, also a vector, indicates the rate of change of velocity over time. In this context, if the acceleration vector points left while the velocity vector points right, it suggests that the object is slowing down, which is essential for predicting the next position and velocity vector.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. This is particularly important in motion analysis, where the next velocity vector must account for both the current velocity and the effect of acceleration. Understanding how to add vectors graphically or mathematically is key to accurately predicting the motion of an object in a given scenario.