What High School Physics Finals Test: The Big Picture
Most high school physics courses — whether conceptual, honors, or AP-preparatory — weight their finals toward the same foundational content: one-dimensional and two-dimensional kinematics, Newton's three laws and free-body diagrams, work, energy, and power, and conservation of energy and momentum. These topics together typically account for 60–80% of a standard final exam.
Physics questions come in two formats. Conceptual questions ask you to explain why something happens or predict an outcome based on physical principles — no numbers involved. Quantitative problems give you known values and ask you to calculate unknowns using equations. Both require the same underlying understanding, but quantitative problems additionally require dimensional analysis, correct unit usage, and careful algebra. Students who struggle most on physics exams typically fall into one of two groups: those who have memorized equations but cannot conceptually interpret what they mean, and those who understand the concepts but cannot execute the algebra cleanly under time pressure. A good study guide addresses both.
Kinematics: Motion in One and Two Dimensions
Kinematics describes motion without asking why that motion occurs — it is purely descriptive. The five kinematic quantities are displacement (Δx), initial velocity (v₀), final velocity (v), acceleration (a), and time (t). The four kinematic equations relate these quantities in every possible combination, so any problem that gives you three of the five can be solved using the appropriate equation.
| Equation | Missing Variable | When to Use | Units Check |
|---|---|---|---|
| v = v₀ + at | Δx (displacement) | When you have v₀, a, t and need v (or vice versa) | m/s = m/s + (m/s²)(s) ✓ |
| Δx = v₀t + ½at² | v (final velocity) | When you have v₀, a, t and need Δx | m = (m/s)(s) + (m/s²)(s²) ✓ |
| v² = v₀² + 2aΔx | t (time) | When you have v₀, a, Δx and need v — time not given or needed | (m/s)² = (m/s)² + 2(m/s²)(m) ✓ |
| Δx = ½(v₀ + v)t | a (acceleration) | When you have v₀, v, t and need Δx — acceleration not given | m = ½(m/s + m/s)(s) ✓ |
For projectile motion (two-dimensional kinematics), the horizontal and vertical components are independent. Horizontal: no acceleration (aₓ = 0), so x = v₀ₓ · t. Vertical: acceleration due to gravity (ay = −9.8 m/s² or −10 m/s² for approximation), using all four kinematic equations. The time in the air is determined entirely by the vertical equations and then used to find horizontal range.
Newton's Three Laws: From Concept to Free-Body Diagram
| Law | Statement | Mathematical Form | Classic Application |
|---|---|---|---|
| First Law (Inertia) | An object at rest stays at rest; an object in motion stays in motion — unless acted on by a net external force | ΣF = 0 ↔ a = 0 | Explain why passengers lurch forward when a car brakes; why a tablecloth can be pulled quickly without disturbing dishes |
| Second Law | The net force on an object equals its mass times acceleration | ΣF = ma (F in N, m in kg, a in m/s²) | Calculate acceleration of a pushed box; find the force needed to stop a moving car in a given distance |
| Third Law (Action-Reaction) | For every action force, there is an equal and opposite reaction force — acting on different objects | F₁₂ = −F₂₁ | Rocket propulsion; why a gun recoils when fired; why you push backward on the floor to walk forward |
Free-body diagrams are the single most tested skill in the forces unit. A correct free-body diagram shows every force acting on the object of interest as a labeled vector arrow. The most common forces to include are: weight (W = mg, pointing straight down), normal force (N, perpendicular to surface), friction (f = μN, opposing motion or tendency of motion), tension (T, along the string toward the attachment point), and applied force (F, in the direction of application).
The procedure for every forces problem: draw the free-body diagram first, define positive and negative directions, write ΣF = ma separately for x and y components, and solve. Students who skip the diagram consistently make sign errors and forget forces.
Work, Energy, and Power: The Essential Equations
| Quantity | Equation | SI Unit | Key Condition or Note |
|---|---|---|---|
| Work (W) | W = Fd·cos(θ) | Joule (J = N·m) | θ is angle between force and displacement; W = 0 if force is perpendicular to motion |
| Kinetic Energy (KE) | KE = ½mv² | Joule (J) | Depends on mass and speed; always positive |
| Gravitational PE (PEg) | PEg = mgh | Joule (J) | h = height above reference level; reference level is arbitrary but must be consistent |
| Elastic PE (PEe) | PEe = ½kx² | Joule (J) | k = spring constant (N/m); x = compression or extension from equilibrium |
| Work-Energy Theorem | W_net = ΔKE | Joule (J) | Net work done on an object equals its change in kinetic energy |
| Conservation of Energy | KE₁ + PE₁ = KE₂ + PE₂ (no friction) or + W_friction | Joule (J) | In a closed system with no non-conservative forces, total mechanical energy is constant |
| Power (P) | P = W/t = Fv | Watt (W = J/s) | Rate of doing work; P = Fv when force and velocity are in the same direction |
Unit Conversion Quick Reference
Unit errors are one of the most common sources of lost points on physics finals. Before plugging any value into an equation, verify that all quantities are in SI base units: meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, and Newtons (N = kg·m/s²) for force.
| From | To | Multiply By |
|---|---|---|
| kilometers (km) | meters (m) | × 1,000 |
| centimeters (cm) | meters (m) | ÷ 100 |
| millimeters (mm) | meters (m) | ÷ 1,000 |
| grams (g) | kilograms (kg) | ÷ 1,000 |
| km/h | m/s | ÷ 3.6 |
| miles per hour (mph) | m/s | × 0.447 |
| minutes (min) | seconds (s) | × 60 |
| hours (h) | seconds (s) | × 3,600 |
| Celsius (°C) | Kelvin (K) | + 273.15 |
| pounds (lb) | Newtons (N) | × 4.448 |
20 Practice Problems: Motion and Energy
Work through these under timed conditions — allow yourself about 3 minutes per problem. Check your work using the answers below. If you miss a problem, build an error card identifying the concept missed and the correct approach.
| # | Problem | Answer |
|---|---|---|
| 1 | A car accelerates from rest to 20 m/s in 8 s. What is its acceleration? | 2.5 m/s² |
| 2 | How far does the car in Problem 1 travel during those 8 s? | 80 m |
| 3 | A ball is dropped from rest from a height of 45 m. How long does it take to hit the ground? (g = 10 m/s²) | 3 s |
| 4 | What is the ball's speed just before hitting the ground (Problem 3)? | 30 m/s |
| 5 | A 5 kg object accelerates at 4 m/s². What net force acts on it? | 20 N |
| 6 | A 60 N net force acts on a 15 kg object. What is its acceleration? | 4 m/s² |
| 7 | A 10 kg box rests on a surface with μ = 0.3. What is the friction force opposing motion? (g = 10 m/s²) | 30 N |
| 8 | What net force is required to push that box at constant velocity? | 30 N (equal to friction; a = 0 at constant velocity) |
| 9 | A 3 kg ball moving at 6 m/s has what kinetic energy? | 54 J |
| 10 | A 2 kg book sits on a shelf 3 m above the floor. What is its gravitational PE? (g = 10 m/s²) | 60 J |
| 11 | If the book falls off the shelf, what is its KE just before hitting the floor? | 60 J (PE fully converts to KE) |
| 12 | How fast is the book moving just before impact? | √60 ≈ 7.75 m/s |
| 13 | A force of 50 N moves an object 10 m. How much work is done? | 500 J |
| 14 | If this work is done in 5 s, what is the power output? | 100 W |
| 15 | A roller coaster car (500 kg) starts at rest at 40 m height. What is its speed at the bottom? (g = 10 m/s²) | √800 ≈ 28.3 m/s |
| 16 | A spring with k = 200 N/m is compressed 0.15 m. What elastic PE is stored? | 2.25 J |
| 17 | A projectile is launched horizontally at 25 m/s from a cliff 80 m high. How long is it in the air? (g = 10 m/s²) | 4 s |
| 18 | How far from the base of the cliff does the projectile land? | 100 m |
| 19 | A 1,200 kg car moving at 20 m/s brakes to a stop. How much work did friction do? | −240,000 J (negative; friction opposes motion) |
| 20 | On a velocity-time graph, a straight line from (0, 10) to (5, 0) represents what type of motion? | Uniform deceleration; a = −2 m/s²; object stops at t = 5 s |
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