AP Physics C: Mechanics 7-Day Cram Plan

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 →