Ch 02: Kinematics in One Dimension

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 02: Kinematics in One Dimension

Problem 6a

Chapter 2, Problem 6a

A particle starts from at and moves with the velocity graph shown in FIGURE EX2.6. Does this particle have a turning point? If so, at what time?

Verified step by step guidance

Step 1: Understand the concept of a turning point. A turning point occurs when the velocity of the particle changes direction, i.e., when the velocity becomes zero and then reverses its sign.

Step 2: Analyze the velocity graph provided. The graph shows the velocity of the particle as a function of time. The velocity starts at 0 m/s, increases to 20 m/s, remains constant, and then decreases back to 0 m/s before becoming negative.

Step 3: Identify the time at which the velocity becomes zero after being positive. From the graph, the velocity decreases linearly and reaches 0 m/s at t = 10 seconds.

Step 4: Check if the velocity becomes negative after t = 10 seconds. The graph shows that the velocity becomes negative after t = 10 seconds, indicating a change in direction.

Step 5: Conclude that the particle has a turning point at t = 10 seconds, as this is the time when the velocity transitions from positive to zero and then to negative.

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Key Concepts

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

Velocity and Turning Points

In physics, a turning point occurs when a particle changes its direction of motion. This is typically indicated by a change in the sign of the velocity. In a velocity-time graph, a turning point is where the velocity crosses the time axis, indicating that the particle has stopped and is about to move in the opposite direction.

Velocity-Time Graph Interpretation

A velocity-time graph visually represents an object's velocity over time. The slope of the graph indicates acceleration, while the area under the curve represents displacement. In this case, the graph shows a constant velocity followed by a decrease, which suggests that the particle is moving at a steady speed before slowing down, potentially indicating a turning point.

Constant Velocity

Constant velocity means that an object is moving at a uniform speed in a straight line, with no acceleration. In the provided graph, the particle maintains a velocity of 20 m/s for a period before decreasing. This constant velocity phase indicates that the particle is not experiencing any net forces acting on it, allowing it to move steadily until it begins to decelerate.

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Related Practice

Textbook Question

A particle starts from x₀ = 10 m at t₀= 0 s and moves with the velocity graph shown in FIGURE EX2.6. What is the object’s position at t = 2 s and 4 s?

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Textbook Question

FIGURE EX2.5 shows the position graph of a particle. Draw the particle’s velocity graph for the interval .

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Textbook Question

FIGURE EX2.8 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat?

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Textbook Question

FIGURE EX2.9 shows the velocity graph of a particle. Draw the particle's acceleration graph for the interval 0 s ≤ t ≤ 4 s.

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Textbook Question

FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at t = 5s

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Textbook Question

FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at t = 30s?

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