Choose the correct motion diagram completed by adding acceleration vectors
The correct answer and explanation is:
iturn0image0turn0image1turn0image3turn0image7To accurately complete a motion diagram by adding acceleration vectors, it’s essential to understand the nature of the object’s motion, as acceleration vectors indicate changes in velocity—both in magnitude and direction. Here’s a step-by-step guide to determine the correct acceleration vectors for various scenarios:
1. Identify the Type of Motion:
- Uniform Linear Motion: If an object moves in a straight line at a constant speed, its velocity remains constant, resulting in zero acceleration. Thus, no acceleration vectors are needed in the motion diagram.
- Linear Acceleration: For an object moving in a straight line with changing speed:
- Speeding Up: The acceleration vector points in the same direction as the velocity vector.
- Slowing Down: The acceleration vector points opposite to the direction of the velocity vector.
- Projectile Motion: An object moving under the influence of gravity alone (e.g., a ball thrown in the air) experiences a constant acceleration vector pointing downward, regardless of its path.
- Uniform Circular Motion: An object moving in a circular path at constant speed has an acceleration vector (centripetal acceleration) pointing toward the center of the circle at all points along its path.
2. Drawing Acceleration Vectors:
- Determine Direction: Based on the motion type, establish the direction of the acceleration vector. For instance, in projectile motion, the acceleration due to gravity always points downward.
- Consistent Representation: Ensure that acceleration vectors are consistently represented at each point in the motion diagram, reflecting the continuous nature of acceleration.
3. Practical Example:
Consider a car accelerating from rest along a straight road:
- Initial State: At rest, the velocity is zero; thus, no acceleration vector is present.
- During Acceleration: As the car speeds up, velocity vectors increase in length in the direction of motion, and acceleration vectors point in the same direction.
- Constant Speed: Once the car reaches a constant speed, velocity vectors remain the same length, and acceleration vectors become zero.
4. Application to the Given Diagram:
Without the specific diagram, a general approach is:
- Analyze Velocity Vectors: Observe the direction and length of velocity vectors to determine changes in speed and direction.
- Add Acceleration Vectors: Based on the analysis:
- If velocity vectors increase in length in the same direction, add acceleration vectors in that direction.
- If velocity vectors decrease in length, add acceleration vectors opposite to the direction of motion.
- For changes in direction (e.g., circular motion), add acceleration vectors pointing toward the center of the curvature.
In summary, accurately completing a motion diagram with acceleration vectors requires a clear understanding of the object’s motion characteristics. By analyzing velocity changes and applying the principles of kinematics, one can correctly depict acceleration vectors, enhancing the diagram’s accuracy and educational value.