gracie ran a $200\text{ m}$ race.
the first part of her race is shown on the distance-time graph below.
she ran the rest of the race at a constant speed of $5\text{ m/s}$.
which of the lines a-d complete the distance-time graph of gracies race?

Question

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-Time Graphs", "Constant Speed Calculation" ], "new_concepts": [], "current_concepts": [ "Distance-Time Graphs", "Constant Speed Calculation" ] } ## Analyze the initial phase of the race Using the *Distance-Time Graphs* knowledge point $$ \begin{aligned} &\text{Initial point: } (0, 0)\ &\text{End of first part: } (15, 100)\ &\text{Distance covered: } 100\text{ m}\ &\text{Time elapsed: } 15\text{ s} \end{aligned} $$ ## Calculate the remaining race parameters Using the *Constant Speed Calculation* knowledge point $$ \begin{aligned} &\text{Total race distance} = 200\text{ m}\ &\text{Remaining distance} = 200\text{ m} - 100\text{ m} = 100\text{ m}\ &\text{Constant speed } (v) = 5\text{ m/s}\ &\text{Remaining time } (\Delta t) = \frac{100\text{ m}}{5\text{ m/s}} = 20\text{ s} \end{aligned} $$ ## Determine the final coordinates on the graph Using the *Distance-Time Graphs* knowledge point $$ \begin{aligned} &t_{\text{final}} = 15\text{ s} + 20\text{ s} = 35\text{ s}\ &d_{\text{final}} = 200\text{ m}\ &\text{Final coordinate: } (35, 200) \end{aligned} $$ ## Identify the matching line on the graph Using the *Distance-Time Graphs* knowledge point $$ \begin{aligned} &\text{Line A ends at: } (20, 200)\ &\text{Line B ends at: } (30, 200)\ &\text{Line C ends at: } (35, 200)\ &\text{Line D ends at: } (40, 200)\ &\text{Matching Line: } \text{C} \end{aligned} $$

(A) Line A

(B) Line B

(C) Line C

(D) Line D

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Distance-Time Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the initial phase of the race

Calculate the remaining race parameters

Determine the final coordinates on the graph

Identify the matching line on the graph

Answer: