Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.61 Particle Motion Displacement and Distance Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.61 Particle Motion Displacement and Distance. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.61 Particle Motion - Displacement and Distance - Choose displacement, total distance, or final position from velocity and initial position information. Aligned to AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.61 Particle Motion Displacement and Distance skill assessments:

Problem 1Difficulty: Mastery
A particle has x(0)=1 and velocity v(t)=t3-6t2+8t for 0 <= t <= 5. Which pair gives x(5) and total distance?
Ax(5)=25/4; total distance=57/4 units
Bx(5)=29/4; total distance=25/4 units
Cx(5)=1; total distance=57/4 units
Dx(5)=29/4; total distance=57/4 units
Solution & Explanation:The velocity factors as t(t-2)(t-4). With F(t)=t4/4-2t3+4t2, the signed displacement is F(5)-F(0)=25/4, so x(5)=1+25/4=29/4. Absolute area over [0,2], [2,4], and [4,5] gives 4+4+25/4=57/4 units.
Problem 2Difficulty: Mastery
Let k > 0 and v(t)=k(t-2) for 0 <= t <= 4. Which statement must be true?
AFinal position is 4k units to the right of initial position.
BDisplacement is 4k units, and total distance is 0.
CFinal position equals initial position, and total distance is 4k units.
DFinal position equals initial position, and total distance is 0.
Solution & Explanation:The signed areas on [0,2] and [2,4] are equal in magnitude and opposite in sign, so displacement is 0 and final position equals initial position. Total distance adds both triangular areas: 2k+2k=4k.
Problem 3Difficulty: Mastery
A particle's velocity is v(t)=4t3-4t for -1 <= t <= 2. What is the total distance traveled?
A9 units
B11 units
C2 units
D13 units
Solution & Explanation:The zeros are t=-1, 0, and 1. With F(t)=t4-2t2, the absolute area contributions are 1, 1, and 9, so the total distance is 11 units. The signed displacement is 9 units.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Choose displacement, total distance, or final position from velocity and initial position information. Aligned to AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.).

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