Question

1. which of the following segments shows the fastest constant velocity?

graph with distance on y-axis, time on x-axis, segments labeled a, b, c, d, e
options: a, b, c, d

Explanation:

Step1: Recall velocity formula

In a distance - time graph, velocity \(v=\frac{\Delta d}{\Delta t}\), where \(\Delta d\) is the change in distance and \(\Delta t\) is the change in time. For a constant velocity, the graph is a straight line (since \(d = vt\), which is a linear equation). The steeper the straight - line segment, the larger the value of \(\frac{\Delta d}{\Delta t}\), and thus the faster the constant velocity.

Step2: Analyze each segment

• Segment A: It is a straight - line segment (constant velocity). We can visually compare the slope of segment A with other straight - line segments (C, E). The slope of segment A (change in distance over change in time) is steeper than that of segment C and segment E.
• Segment B: It is a curved segment, which means the velocity is changing (acceleration is non - zero), so it does not represent constant velocity.
• Segment C: It is a straight - line segment but less steep than segment A.
• Segment D: It is a horizontal segment, which means \(\Delta d = 0\) (velocity \(v = 0\), object is at rest).
• Segment E: It is a straight - line segment (constant velocity, but in the negative direction, representing deceleration or motion in the opposite direction). The magnitude of its slope (speed) is less than that of segment A.

Answer:

A. A