Question

the graph shows marc’s distance from a motion detector with respect to time. based on the graph, which of the following statements is true?
distance from motion detector vs. time
graph with distance (feet) on y - axis (1 - 9) and time (seconds) on x - axis (1 - 9), with points a, b, c, d and a blue line connecting them
options:

• the fastest marc walked was when he was walking towards the motion detector.
• marc was walking away from the motion detector for a total of 7 seconds.
• marc stood still for 3 seconds.
• marc spent most of the time during his walk walking towards the motion detector.

Explanation:

Step1: Analyze slope meaning

In a distance - time graph, the slope represents speed. A positive slope means moving away from the detector (distance increasing with time), a negative slope means moving towards the detector (distance decreasing with time), and a zero slope means standing still.

Step2: Evaluate each option

• Option 1: Check slopes. The slope when moving towards (negative slope, from \(t = 7\) to \(t = 8\)) has a steeper slope (greater absolute value) than the slopes when moving away (positive slopes). So the fastest speed is when moving towards.
• Option 2: Time moving away: From \(t = 0\) to \(t = 6\), that's 6 seconds, not 7. So this is wrong.
• Option 3: Standing still is when slope is zero (from \(t = 5\) to \(t = 7\)), which is 2 seconds, not 3. Wrong.
• Option 4: Time moving towards: from \(t = 7\) to \(t = 8\) (1 second). Time moving away: from \(t = 0\) to \(t = 6\) (6 seconds). So most time is moving away. Wrong.

Answer:

The fastest Marc walked was when he was walking towards the motion detector.