Ch 01: Concepts of Motion

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 01: Concepts of Motion

Problem 10b

Chapter 1, Problem 10b

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 points left.

Verified step by step guidance

Step 1: Analyze the given motion diagram. Dot 3 represents the current position, and the velocity vector V₃ points to the right, indicating motion in that direction. The acceleration vector at dot 3 is specified to point left, meaning the object is decelerating as it moves to the right.

Step 2: Understand the effect of the leftward acceleration. Since acceleration is opposite to the direction of velocity, the magnitude of the velocity will decrease as the object moves from dot 3 to dot 4.

Step 3: Predict the position of dot 4. Since the object is still moving to the right but slowing down, dot 4 will be placed to the right of dot 3, but closer to dot 3 compared to the distance between dots 2 and 3.

Step 4: Draw the velocity vector at dot 4. The velocity vector at dot 4 will still point to the right but will be shorter in length compared to V₃, reflecting the reduced speed due to the leftward acceleration.

Step 5: Add the acceleration vector at dot 3 to the diagram. The acceleration vector should be drawn pointing left at dot 3 to indicate the deceleration effect.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Motion Diagrams

Motion diagrams visually represent the position of an object at various time intervals. Each dot in the diagram indicates the object's position at a specific moment, while arrows represent velocity vectors, showing the direction and magnitude of motion. Understanding motion 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 the context of the question, the relationship between velocity and acceleration is essential, as acceleration can affect the object's speed and direction, particularly when it points in the opposite direction of the velocity.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. This is particularly important in physics when analyzing motion, as both velocity and acceleration are vectors. In the given scenario, understanding how to add the acceleration vector to the existing velocity vector will help determine the new velocity vector for dot 4, especially since the acceleration is directed opposite to the velocity.

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Related Practice

Textbook Question

A speed skater accelerates from rest and then keeps skating at a constant speed. Draw a complete motion diagram of the skater.

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Textbook Question

You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the ball's position and average velocity vectors from the time you release the ball until the instant it touches the ground.

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Textbook Question

FIGURE EX1.9 shows five points of a motion diagram. Use Tactics Box 1.2 to find the average acceleration vectors at points 1, 2, and 3. Draw the completed motion diagram showing velocity vectors and acceleration vectors.

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Textbook Question

Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a complete motion diagram of the tennis ball from the time it is released until it reaches the maximum height on its bounce. Be sure to determine and show the acceleration at the lowest point.

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Textbook Question

FIGURE EX1.8 shows the first three points of a motion diagram. Is the object's average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1? Explain how you can tell.

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Textbook Question

A bowling ball rolls up an incline and then onto a smooth, level surface. Draw a complete motion diagram of the bowling ball. Don't try to find the acceleration vector at the point where the motion changes direction; that's an issue for Chapter 4.

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