Displacement from a velocity graph Consider the velocity function for an object moving along a line (see figure).
(a) Describe the motion of the object over the interval [0,6].

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Observe the velocity graph, which shows the velocity of the object (in m/s) as a function of time (in seconds). The graph consists of linear segments over the interval [0,6].

From t=0 to t=1, the velocity increases linearly from 0 m/s to 20 m/s. This indicates the object is accelerating uniformly during this time.

From t=1 to t=3, the velocity remains constant at 20 m/s. This indicates the object is moving at a constant velocity, covering equal distances in equal time intervals.

From t=3 to t=5, the velocity decreases linearly from 20 m/s to 10 m/s. This indicates the object is decelerating uniformly during this time.

From t=5 to t=6, the velocity remains constant at 10 m/s. This indicates the object is moving at a constant velocity again, but at a slower speed compared to the interval [1,3].

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주요 개념

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

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both speed and direction. In the context of the graph, the velocity values indicate how fast the object is moving at different times, which is crucial for understanding its motion.

Displacement

Displacement is the overall change in position of an object, calculated as the area under the velocity-time graph. It can be positive, negative, or zero, depending on the direction of motion. By analyzing the graph, one can determine the total displacement over the interval [0,6] seconds by summing the areas of the shapes formed under the curve.

Intervals of Motion

Intervals of motion refer to specific time segments during which the object's velocity remains constant or changes. In the given graph, different segments indicate periods of acceleration, constant velocity, and deceleration. Understanding these intervals helps in describing the object's motion accurately over the specified time frame.

Displacement from a velocity graph Consider the velocity function for an object moving along a line (see figure).(a) Describe the motion of the object over the interval [0,6].