The position of an object along a straight tunnel as a function of time is plotted in Fig. 2–40. What is its average velocity between t = 25.0 s and t = 30.0 s?

검증된 단계별 안내

Identify the formula for average velocity: \( v_{\text{avg}} = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is the change in position and \( \Delta t \) is the change in time.

From the problem, the time interval is given as \( t_1 = 25.0 \ \text{s} \) and \( t_2 = 30.0 \ \text{s} \). Determine the corresponding positions \( x_1 \) and \( x_2 \) from the graph provided in the figure.

Calculate the change in position: \( \Delta x = x_2 - x_1 \). Substitute the values of \( x_2 \) and \( x_1 \) obtained from the graph.

Calculate the change in time: \( \Delta t = t_2 - t_1 \). Substitute \( t_2 = 30.0 \ \text{s} \) and \( t_1 = 25.0 \ \text{s} \).

Substitute \( \Delta x \) and \( \Delta t \) into the formula for average velocity: \( v_{\text{avg}} = \frac{\Delta x}{\Delta t} \). Simplify the expression to find the average velocity.

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주요 개념

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

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. It provides a measure of how fast an object is moving in a specific direction over a given time interval. In this case, to find the average velocity between two time points, one must determine the change in position of the object during that time and divide it by the time elapsed.

Displacement

Displacement is a vector quantity that refers to the change in position of an object. It is calculated as the final position minus the initial position and takes into account the direction of movement. In the context of the question, knowing the positions of the object at t = 25.0 s and t = 30.0 s is essential to calculate the displacement needed for the average velocity.

Time Interval

The time interval is the duration over which an event occurs, measured as the difference between two time points. In this question, the time interval is from t = 25.0 s to t = 30.0 s, which is 5 seconds. Understanding the time interval is crucial for calculating average velocity, as it provides the denominator in the average velocity formula.