High School · Physics · Finals Prep

Physics Study Guides: Motion and Energy for High School Finals

Updated February 2026 · 14 min read · By the StudyGuidesAI Editorial Team
For juniors who feel behind: Physics is the most commonly feared science course in high school, and most of that fear is unnecessary. The core of a typical high school physics final — kinematics, Newton's laws, and energy — follows a small number of equations applied to a wide variety of problems. This guide gives you every formula you need, a kinematics and forces reference table, 20 practice problems with answers, unit conversion rules, graph interpretation tips, and a direct path to personalized study guides via StudyGuidesAI.

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.

Graph Interpretation: Position, Velocity, and Acceleration A position-time graph's slope at any point equals velocity. A velocity-time graph's slope equals acceleration, and its area under the curve equals displacement. An acceleration-time graph's area equals the change in velocity. These three relationships appear on virtually every physics final in some form — knowing them eliminates an entire category of questions.

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.

FromToMultiply 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/hm/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.

#ProblemAnswer
1A car accelerates from rest to 20 m/s in 8 s. What is its acceleration?2.5 m/s²
2How far does the car in Problem 1 travel during those 8 s?80 m
3A 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
4What is the ball's speed just before hitting the ground (Problem 3)?30 m/s
5A 5 kg object accelerates at 4 m/s². What net force acts on it?20 N
6A 60 N net force acts on a 15 kg object. What is its acceleration?4 m/s²
7A 10 kg box rests on a surface with μ = 0.3. What is the friction force opposing motion? (g = 10 m/s²)30 N
8What net force is required to push that box at constant velocity?30 N (equal to friction; a = 0 at constant velocity)
9A 3 kg ball moving at 6 m/s has what kinetic energy?54 J
10A 2 kg book sits on a shelf 3 m above the floor. What is its gravitational PE? (g = 10 m/s²)60 J
11If the book falls off the shelf, what is its KE just before hitting the floor?60 J (PE fully converts to KE)
12How fast is the book moving just before impact?√60 ≈ 7.75 m/s
13A force of 50 N moves an object 10 m. How much work is done?500 J
14If this work is done in 5 s, what is the power output?100 W
15A 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
16A spring with k = 200 N/m is compressed 0.15 m. What elastic PE is stored?2.25 J
17A 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
18How far from the base of the cliff does the projectile land?100 m
19A 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)
20On 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

Generate Your Physics Study Guide by Topic

Paste your physics class notes on kinematics, forces, energy, or any other topic. StudyGuidesAI builds a structured guide with equations, worked examples, and targeted practice problems — organized exactly the way your final exam tests them.

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Frequently Asked Questions: For Juniors Who Are Struggling

I understand physics in class but blank out on tests. What do I do?
This is extremely common and almost always reflects insufficient practice under test conditions. Understanding in class means you can follow someone else's reasoning — which is not the same as being able to produce your own reasoning under time pressure. The fix is timed problem practice: set a timer for 3 minutes per problem and work through problems without looking at your notes. Do this three to four times per week leading up to the final. The discomfort of timed self-testing is exactly what prepares your brain for exam conditions.
What are the most important formulas to memorize for a physics final?
Prioritize these in order: the four kinematic equations, ΣF = ma (Newton's second law), W = Fd·cos(θ), KE = ½mv², PEg = mgh, and conservation of energy (KE₁ + PE₁ = KE₂ + PE₂). If your course also covered momentum, add p = mv and the impulse-momentum theorem (J = Δp = FΔt). These eight to ten formulas cover the vast majority of quantitative problems on a typical high school physics final.
How do I approach a physics problem I have never seen before?
Use this four-step approach: (1) Draw a diagram — free-body diagram for force problems, position diagram for kinematics. (2) List knowns and unknowns — write down every value given and label the quantity you need to find. (3) Choose an equation — find the equation that relates your knowns to your unknown. (4) Solve and check — substitute values, solve for the unknown, and verify that your answer has the correct units and a physically reasonable magnitude. Most physics problems that feel impossible become solvable once you complete step 2 carefully.
My teacher moves really fast and I can't follow the board work. How do I catch up?
During class, write down every equation and diagram your teacher writes without trying to fully understand it in the moment. Understanding comes from working problems, not watching them. After class, paste your notes into StudyGuidesAI and generate a concept summary with worked examples — this converts fragmented class notes into a structured study guide. Then work through three to five problems on the topic yourself, checking your work against the guide. This after-class workflow typically takes 30 to 40 minutes and replaces the confusion that builds up when students let incomplete understanding accumulate across multiple lectures.
Is there a way to check my answers without the solution manual?
Yes — dimensional analysis. After solving any physics problem, verify that your final answer has the correct units for the quantity you were solving for. If you were solving for velocity and your answer came out in kg·m (rather than m/s), something went wrong algebraically. If units check out, verify the magnitude is physically reasonable: a car's acceleration should not be 500 m/s²; a person's weight should not be 3,000 N. These sanity checks catch the majority of algebra and sign errors without requiring an answer key.