Understanding Motion from Graphs

The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.

d. When does the particle stand still for more than an instant?

검증된 단계별 안내

Examine the graph of velocity v = f(t) over time t. The particle stands still when its velocity is zero.

Identify the sections of the graph where the velocity is zero. These are the points where the graph intersects the horizontal axis (v = 0).

Observe the graph and note that the velocity is zero between t = 4 seconds and t = 5 seconds.

Since the velocity is zero for a duration from t = 4 to t = 5 seconds, the particle stands still for more than an instant during this interval.

Conclude that the particle stands still for more than an instant between t = 4 seconds and t = 5 seconds.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Velocity and Motion

Velocity is the rate of change of position with respect to time, indicating how fast and in what direction an object is moving. In the context of the graph, the velocity function v = f(t) shows how the particle's speed varies over time. When the velocity is zero, the particle is momentarily at rest, which is crucial for determining when it stands still.

Graph Interpretation

Interpreting graphs involves understanding the relationship between the axes and the data represented. In this case, the x-axis represents time (t in seconds), while the y-axis represents velocity (v). Analyzing the graph allows us to identify intervals where the velocity is zero, indicating when the particle is at rest, and to determine if it remains at rest for more than an instant.

Critical Points and Intervals

Critical points in a function occur where the function's value is zero or undefined, which in this case relates to the velocity function. By identifying these points on the graph, we can determine intervals where the particle is stationary. If the velocity remains zero over an interval rather than just at isolated points, the particle stands still for more than an instant.

Understanding Motion from GraphsThe accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.d. When does the particle stand still for more than an instant?