determine whether each statement is true or false.

the speed of trolley a is equal to the speed of trolley c.
the speed of trolley a is less than the speed of trolley b.
the speed of trolley b is equal to the speed of trolley a.
the speed of trolley d is greater than the speed of trolley a.

Question

determine whether each statement is true or false.

the speed of trolley a is equal to the speed of trolley c.
the speed of trolley a is less than the speed of trolley b.
the speed of trolley b is equal to the speed of trolley a.
the speed of trolley d is greater than the speed of trolley a.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Speed Calculation", "Speed Comparison" ], "new_concepts": [], "current_concepts": [ "Speed Calculation", "Speed Comparison", "Motion Models" ] } ## Calculate speed of each trolley from the graphs $$ \begin{aligned} &v_A = \frac{90\text{ mi}}{6\text{ h}} = 15\text{ mph}\ &v_B = \frac{120\text{ mi}}{6\text{ h}} = 20\text{ mph}\ &v_C = \frac{60\text{ mi}}{4\text{ h}} = 15\text{ mph}\ &v_D = \frac{60\text{ mi}}{3\text{ h}} = 20\text{ mph} \end{aligned} $$ ## Evaluate each statement $$ \begin{aligned} &\text{Statement 1: } v_A = v_C \implies 15 = 15 \quad (\text{True})\ &\text{Statement 2: } v_A < v_B \implies 15 < 20 \quad (\text{True})\ &\text{Statement 3: } v_B = v_A \implies 20 = 15 \quad (\text{False})\ &\text{Statement 4: } v_D > v_A \implies 20 > 15 \quad (\text{True}) \end{aligned} $$ ## Question 1 The speed of trolley A is equal to the speed of trolley C. **True** ## Question 2 The speed of trolley A is less than the speed of trolley B. **True** ## Question 3 The speed of trolley B is equal to the speed of trolley A. **False** ## Question 4 The speed of trolley D is greater than the speed of trolley A. **True** { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Speed Calculation" ] }

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Question

Explanation:

Calculate speed of each trolley from the graphs

Evaluate each statement

Answer:

Question 1

Question 2

Question 3

Question 4