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

검증된 단계별 안내

Step 1: Understand the problem. The velocity of the bicycle at a specific time can be determined from the slope of the position-versus-time graph at that time. Velocity is the rate of change of position with respect to time.

Step 2: Recall the formula for velocity from a position-time graph: \( v = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is the change in position and \( \Delta t \) is the change in time. The slope of the graph at a given point represents the instantaneous velocity.

Step 3: Locate \( t = 5 \, \text{s} \) on the graph. Identify the segment of the graph that corresponds to this time and determine whether the graph is linear or curved at this point.

Step 4: If the graph is linear at \( t = 5 \, \text{s} \), calculate the slope of the line by selecting two points on the line near \( t = 5 \, \text{s} \). Use the formula \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \), where \( y \) represents position and \( x \) represents time.

Step 5: If the graph is curved at \( t = 5 \, \text{s} \), draw a tangent line to the curve at \( t = 5 \, \text{s} \). Calculate the slope of this tangent line using the same formula \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \). This slope represents the instantaneous velocity at \( t = 5 \, \text{s} \).

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주요 개념

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Position vs. Time Graph

A position vs. time graph visually represents an object's position over time. The x-axis typically represents time, while the y-axis represents position. The slope of the graph at any point indicates the object's velocity, with a steeper slope corresponding to a higher velocity.

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 a position vs. time graph, velocity can be determined by calculating the slope of the tangent line at a specific point on the graph.

Tangent Line

A tangent line is a straight line that touches a curve at a single point without crossing it. In the context of a position vs. time graph, the slope of the tangent line at a given time indicates the instantaneous velocity of the object at that moment. This is crucial for determining how fast the bicycle is moving at t = 5s.