the following graph shows the distance vs time relationships of 3 runners. which of the three runners sped up during the race?

none of them sped up
red
blue
green

Question

the following graph shows the distance vs time relationships of 3 runners. which of the three runners sped up during the race?

none of them sped up
red
blue
green

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distance-Speed-Time", "Linear Modeling", "Slope-Intercept Form" ], "new_concepts": [ "Position-Time Graph Analysis", "Instantaneous Velocity Interpretation" ], "current_concepts": [ "Distance-Speed-Time", "Linear Modeling", "Slope-Intercept Form", "Position-Time Graph Analysis", "Instantaneous Velocity Interpretation" ] } ## Relate slope to speed Using the *Distance-Speed-Time* and *Linear Modeling* knowledge points $$ v = \frac{d(d)}{dt} = \text{slope of the distance-time graph} $$ ## Analyze the green runner's motion Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &\text{The green line is straight from } t = 0 \text{ to } t \approx 34\text{ s.}\ &\text{Slope is constant, so speed is constant.} \end{aligned} $$ ## Analyze the red runner's motion Using the *Linear Modeling* knowledge point $$ \begin{aligned} &\text{From } t = 0 \text{ to } t = 9\text{ s: slope } \approx \frac{50}{9} \approx 5.56\text{ m/s.}\ &\text{From } t = 9 \text{ to } t = 34\text{ s: slope } \approx \frac{100-50}{34-9} = 2\text{ m/s.}\ &\text{The slope decreased, meaning the red runner slowed down.} \end{aligned} $$ ## Analyze the blue runner's motion Using the *Linear Modeling* knowledge point $$ \begin{aligned} &\text{From } t = 0 \text{ to } t = 20\text{ s: slope } \approx \frac{60}{20} = 3\text{ m/s.}\ &\text{From } t = 20 \text{ to } t = 26\text{ s: slope } \approx \frac{100-60}{26-20} \approx 6.67\text{ m/s.}\ &\text{The slope increased, meaning the blue runner sped up.} \end{aligned} $$

None of them sped up

(B) Red

(C) Blue

(D) Green

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Physics", "Kinematics Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Relate slope to speed

Analyze the green runner's motion

Analyze the red runner's motion

Analyze the blue runner's motion

Answer: