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

Verified step by step guidance

1. Step 1: Understand that a turning point occurs when the velocity changes direction, i.e., when the velocity crosses the time axis (v = 0).
2. Step 2: Analyze the velocity-time graph provided. The graph shows the velocity of the particle over time.
3. Step 3: Observe that the velocity is positive from t = 0 to t = 8 seconds, and then it becomes negative after t = 8 seconds.
4. Step 4: Identify the point where the velocity crosses the time axis. This occurs at t = 10 seconds, where the velocity is zero.
5. Step 5: Conclude that the particle has a turning point at t = 10 seconds, as this is where the velocity changes direction.

Key Concepts

Velocity-Time Graph

A velocity-time graph illustrates how the velocity of an object changes over time. The y-axis represents velocity, while the x-axis represents time. The shape of the graph indicates the object's motion; for instance, a horizontal line indicates constant velocity, while a slope indicates acceleration or deceleration. Analyzing the graph helps determine key features such as turning points, where the velocity changes direction.

Turning Point

A turning point in motion occurs when an object changes its direction of travel, which is indicated by a change in the sign of its velocity. In a velocity-time graph, this is represented by the velocity crossing the time axis (from positive to negative or vice versa). Identifying the time at which this occurs is crucial for understanding the motion of the particle and predicting its future trajectory.

Constant Velocity

Constant velocity means that an object moves at a steady speed in a straight line, with no acceleration. In a velocity-time graph, this is depicted as a horizontal line. The particle in the given graph maintains a constant velocity of 20 m/s for a period before decelerating, which is essential for determining the time intervals of motion and any subsequent changes in direction.