Question

use the letters on the graph to answer the following questions
8 in which segment did the car move the fastest?
how do you know?

9 in what segment was the car stopped?
how do you know?

10 in what segment did the car’s slowest moving speed occur? (not zero)
how do you know?

11 describe the difference between the total distance traveled and the displacement of an object.

Explanation:

Question 8

Step1: Recall speed from distance - time graph

In a distance - time graph, the speed of an object is given by the slope of the graph, where \( \text{slope}=\frac{\text{change in distance}}{\text{change in time}} \). A steeper slope indicates a higher speed.

Step2: Analyze each segment

• Segment A: The slope here is relatively steep as the distance changes rapidly with respect to time.
• Segment B: The slope is zero (horizontal line), so speed is zero.
• Segment C: The slope is less steep than segment A.
• Segment D: The slope is the least steep among the non - zero slope segments.

So, the car moves the fastest in segment A because the slope of the distance - time graph (which represents speed) is the steepest in segment A.

Step1: Recall speed from distance - time graph

In a distance - time graph, when the graph is a horizontal line (slope = 0), the distance does not change with time. Since \( \text{speed}=\frac{\text{change in distance}}{\text{change in time}} \), if the change in distance is zero, speed is zero (the object is stopped).

Step2: Identify the horizontal segment

Looking at the graph, segment B is a horizontal line. So, the distance remains constant as time passes.

Step1: Recall speed from distance - time graph

Speed is the slope of the distance - time graph (\( \text{slope}=\frac{\text{change in distance}}{\text{change in time}} \)). The less steep the slope (for non - zero slope segments), the lower the speed.

Step2: Analyze non - zero slope segments

• Segment A: Steep slope (high speed).
• Segment C: Moderate slope.
• Segment D: Least steep slope among non - zero slope segments.

So, the car's slowest non - zero speed occurs in segment D because the slope of the distance - time graph (speed) is the least steep (smallest) in segment D.

Answer:

A; Because the slope of the distance - time graph (speed) is the steepest in segment A.

Question 9