Question

1. enter your answer.

use the description and the graph to answer the question.
can you draw any conclusions about the distances traveled during the intervals?
explain.

Explanation:

To determine distances traveled during intervals (assuming constant speed as in the sample for speed), we use the formula \( \text{Distance} = \text{Speed} \times \text{Time} \). If we know the speed during each interval and the time duration of each interval:

• If one interval has a greater speed and a longer (or equal) time, it travels a greater distance.
• If speed is constant in each interval, we compare \( \text{Speed}_1 \times \text{Time}_1 \) and \( \text{Speed}_2 \times \text{Time}_2 \). For example, if interval F has higher speed and the time intervals are known (or if we assume time from the graph’s x - axis), we can conclude. Suppose interval F has speed \( v_F \), interval E has speed \( v_E \), and time durations \( t_F, t_E \). If \( v_F>v_E \) and \( t_F\geq t_E \), distance in F is greater. If time info is from the graph (e.g., steeper slope for F means higher speed, and if time length is same, F travels more; if time is different, we need both speed and time).

Answer:

To draw conclusions about the distances traveled during the intervals, we use the formula \( \boldsymbol{\text{Distance} = \text{Speed} \times \text{Time}} \). If the car travels at constant speeds (\( v_1 \) and \( v_2 \)) during two intervals with time durations \( t_1 \) and \( t_2 \):

• If we know \( v_1 > v_2 \) (e.g., from a steeper slope on a distance - time graph, as in the speed - related sample) and \( t_1 \geq t_2 \), the interval with higher speed (\( v_1 \)) travels a greater distance (\( v_1t_1>v_2t_2 \)).
• If the time durations are equal, the interval with the higher speed travels a greater distance. If speed is constant in each interval, we must compare both speed and time. For example, if interval F (from the sample’s context) has a higher speed and the time duration of F is at least as long as the other interval, F travels a greater distance. Without specific time data, we can still say that distance depends on both speed and time; if speed is higher in one interval, a longer time in that interval (or equal time) will mean a greater distance.