AP Physics C: Mechanics 7-Day Cram Plan

title: "AP Physics C: Mechanics 7-Day Cram Plan" description: "A week-long AP Physics C: Mechanics study plan covering all 7 units, daily problem sets, and a full mock exam on Day 7." date: "2026-01-15" examDate: "May AP Exam" topics:

• Kinematics
• Newton's Laws
• Work and Energy
• Momentum
• Rotation
• Oscillations
• Gravitation

You have seven days until the AP Physics C: Mechanics exam. This plan structures your time unit-by-unit, hitting all 7 CED units with daily targets. Each day includes concept review (30 min), worked examples (45 min), and independent practice (90 min).

Total: ~2.75 hours per day. If you have more time, repeat practice sets; if less, reduce the problem count but keep all seven units.

Daily Study Plan

| Day | Unit | Focus | Review Time | Practice | |---|---|---|---|---| | 1 | Kinematics | $v = dx/dt$, $a = dv/dt$, integration to find $v(t)$ and $x(t)$ from $a(t)$ | 30 min | 15 MCQs, 1 kinematics FRQ (projectile motion) | | 2 | Newton's Laws | Free body diagrams, $\\Sigma F = ma$ in components, friction, constraint forces | 30 min | 15 MCQs, 1 dynamics FRQ (inclined plane with friction) | | 3 | Work and Energy | $W = \\int F \\, dx$, $F = -dU/dx$, work-energy theorem, mechanical energy conservation | 30 min | 15 MCQs, 1 energy FRQ (with friction or at two heights) | | 4 | Momentum and Impulse | $p = mv$, $J = \\Delta p = \\int F \\, dt$, conservation in collisions (elastic and inelastic) | 30 min | 15 MCQs, 1 momentum FRQ (collision or explosion) | | 5 | Rotation | $I = \\int r^2 \\, dm$, parallel-axis theorem, $\\tau = I\\alpha$, $L = I\\omega$, conservation of angular momentum | 30 min | 15 MCQs, 1 rotation FRQ (moment of inertia or angular momentum) | | 6 | Oscillations and Gravitation | SHM: $\\ddot{x} + \\omega^2 x = 0$, $T = 2\\pi\\sqrt{m/k}$; Gravitation: $F = GMm/r^2$, escape velocity, orbits | 60 min | 20 MCQs (10 oscillation, 10 gravitation), 1–2 worked examples | | 7 | Mock Exam | Full-length: 35 MCQ (timed, 45 min) + 3 FRQ (timed, 45 min) | — | Timed exam, then review |

Daily Structure Example (Day 1: Kinematics)

Concept Review (30 min)

Read or skim:

• Definition: $v = dx/dt$ means velocity is the rate of change of position with respect to time.
• Definition: $a = dv/dt$ means acceleration is the rate of change of velocity.
• To find $v(t)$ from $a(t)$: integrate: $v(t) = v_0 + \\int_0^t a(\\tau) \\, d\\tau$.
• To find $x(t)$ from $v(t)$: integrate: $x(t) = x_0 + \\int_0^t v(\\tau) \\, d\\tau$.
• Example: if $a(t) = 10 \\, \\text{m/s}^2$ (constant), then $v(t) = v_0 + 10t$ and $x(t) = x_0 + v_0 t + 5t^2$.

💡 Tip: The exam will give you $a(t)$ (as a function or a graph) and ask you to find $v$ at some time, or $x$ at some time, or when the object returns to the origin. Every time, integrate.

Worked Examples (45 min)

Example 1: A car starts from rest with $a(t) = 2 \\, \\text{m/s}^2$ for $t \\in [0, 5]$ seconds, then $a(t) = 0$ for $t > 5$. Find $v(5)$, $x(5)$, and $x(10)$.

Solution:

• $v(5) = 0 + \\int_0^5 2 \\, dt = 10 \\, \\text{m/s}$.
• $x(5) = 0 + \\int_0^5 v(t) \\, dt = \\int_0^5 2t \\, dt = [t^2]_0^5 = 25 \\, \\text{m}$.
• From $t = 5$ to $t = 10$: $v = 10$ (constant), so $x(10) = 25 + 10 \\cdot 5 = 75 \\, \\text{m}$.

Example 2: A ball is thrown straight up with $v_0 = 20 \\, \\text{m/s}$. Taking $a(t) = -10 \\, \\text{m/s}^2$ (gravity), find when $v = 0$ (peak), and the height at peak.

Solution:

• $v(t) = 20 - 10t$. Set $v = 0$: $t = 2 \\, \\text{s}$.
• $x(t) = 20t - 5t^2$. At $t = 2$: $x(2) = 40 - 20 = 20 \\, \\text{m}$.

Independent Practice (90 min)

Do 15 MCQs covering:

• Given $v(t)$ on a graph, identify regions where $a > 0$ (curve concave up).
• Given $a(t)$, integrate to find $v(t)$.
• Projectile motion in 2D: separate into $x$ and $y$ components.

Then tackle one full kinematics FRQ: typically projectile motion with multiple parts (find landing time, maximum height, etc.). Show all integrals.

Repeat for Days 2–6

Each day follows the same rhythm: 30 min review, 45 min worked examples, 90 min independent practice. Adjust the problem count if time is short, but hit all topics.

Day 7: Full Mock Exam (3 hours)

Set a timer. Do not stop or peek at solutions mid-exam.

Multiple-Choice (45 min, no calculator section listed, so treat as mixed)

• 35 questions spanning all 7 units.
• Aim to finish in 40 min, leaving 5 min to guess on blanks.

Free Response (45 min)

• 3 FRQs, each 15 min.
• Solve in order; do not skip.
• Show all work: FBDs, integral setups, conservation statements.

After the exam

• Score your MCQ. Each correct = 1.2 points (raw); 35 correct = 42 points.
• Grade your FRQs using the official rubric (typically 9 points each).
• Total raw score out of ~75. Rough scaling: 50–60% = 5 (depends on year).

⚠️ Important: Physics C is curved generously. Scoring 50–55% raw can earn a 5. Do not panic if you leave questions blank.

Topics by day — high-yield emphasis

| Unit | Must-Know | Tricky Part | Exam Frequency | |---|---|---|---| | Kinematics | Integration: $a(t) \\to v(t) \\to x(t)$ | Sign of acceleration; graphing | 2–3 MCQs, 1 FRQ | | Newton's Laws | FBD + components, $\\Sigma F = ma$ | Normal force direction; friction | 3–4 MCQs, 1 FRQ | | Energy | $W = \\int F \\, dx$, conservation with friction | Negative work; energy diagrams | 3–4 MCQs, 1–2 FRQs | | Momentum | $p = mv$, impulse-momentum, collisions | Distinguishing elastic vs. inelastic | 3–4 MCQs, 1 FRQ | | Rotation | $I = \\int r^2 \\, dm$, parallel axis, $L = I\\omega$ | Choosing the right pivot; rolling vs. spinning | 3–4 MCQs, 1 FRQ | | Oscillation | $T = 2\\pi\\sqrt{m/k}$, SHM from $\\ddot{x} = -\\omega^2 x$ | Energy in SHM; phase and amplitude | 2–3 MCQs, 0–1 FRQ | | Gravitation | Escape velocity, orbital mechanics, Kepler | Sign of potential energy; orbits vs. escape | 2–3 MCQs, 0–1 FRQ |

Study tips for the week

• Don't skip FBDs. Even if you run short on time, draw them on every practice problem.
• Learn one worked example cold per unit. Be able to talk through it step-by-step.
• Flag your weak spots after Day 1 and spend Day 6 there before the mock.
• Sleep 7–8 hours each night. Memory consolidation is real.

Ready to start? Jump to Day 1: Kinematics →