ExamFinch.com My Study

Study guide

8.1 Mechanics: Motion, Newton's Laws, Work, and Energy

Practice this exam

Adamson University College Entrance Test AdUCET

Track your progress as you read

Finished sections get a check mark.

1 Introduction & Exam Overview

1.1 AdUCET Overview, Format, and Admission Process 1.2 Test-Taking and Time-Management Strategies

2 Chapter 2: Mathematics I — Numbers, Algebra, and Functions

2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions 2.2 Algebra, Polynomials, and Linear/Quadratic Equations 2.3 Inequalities, Absolute Value, and Systems of Equations 2.4 Radicals, Rational Expressions, and Scientific Notation 2.5 Coordinate Geometry, Lines, and Functions

3 Chapter 3: Mathematics II — Geometry, Measurement, and Trigonometry

3.1 Plane Geometry: Angles, Triangles, Polygons, and Circles 3.2 Solid Mensuration, Measurement, and Unit Conversion 3.3 Right-Triangle Trigonometry and Applications

4 Chapter 4: Mathematics III — Sequences, Proportion, and Data

4.1 Arithmetic and Geometric Sequences and Series 4.2 Ratio, Proportion, Percentage, Work, and Mixture Problems 4.3 Descriptive Statistics and Data Interpretation 4.4 Probability: Rules, Compound Events, and Conditional Probability 4.5 Counting Principles: Permutations and Combinations

5 Chapter 5: English I — Reading Comprehension and Vocabulary

5.1 Reading Comprehension: Main Idea, Purpose, and Passage Structure 5.2 Inference, Supporting Detail, and Author's Tone 5.3 Word Roots, Prefixes, and Suffixes 5.4 Vocabulary in Context, Synonyms, Antonyms, and Confusables

6 Chapter 6: English II — Grammar, Usage, and Written Expression

6.1 Subject-Verb Agreement and Verb Tenses 6.2 Pronouns, Modifiers, and Parallel Structure 6.3 Sentence Boundaries, Clauses, and Punctuation 6.4 Sentence Correction, Redundancy, and Idiomatic Usage 6.5 Verbal Analogies and Relationship Bridges 6.6 Paragraph Organization, Coherence, and Transitions

7 Chapter 7: General Science I — Biology and Chemistry

7.1 Cell Biology, Transport, and Cellular Energetics 7.2 Genetics, Heredity, and Molecular Biology 7.3 Human Body Systems, Ecology, and Evolution 7.4 Matter, Phase Changes, and Atomic Structure 7.5 Periodic Trends, Chemical Bonding, Reactions, Acids and Bases

8 Chapter 8: General Science II — Physics and Earth Science

8.1 Mechanics: Motion, Newton's Laws, Work, and Energy 8.2 Waves, Sound, Light, Heat, Electricity, and Magnetism 8.3 Earth's Structure, Plate Tectonics, and the Rock Cycle 8.4 The Atmosphere, Weather, the Water Cycle, and Astronomy

9 Chapter 9: Aptitude and Abstract Reasoning

9.1 Figure Series and Pattern Progression 9.2 Matrix Reasoning and Figural Analogies 9.3 Spatial Reasoning: Rotation, Reflection, and Chirality 9.4 Paper Folding, Cube Nets, and Orthographic Views 9.5 Deductive Reasoning, Syllogisms, and Venn Diagrams 9.6 Number, Letter, and Alphanumeric Series 9.7 Odd-One-Out, Classification, and Logic Puzzles

8.1 Mechanics: Motion, Newton's Laws, Work, and Energy

Key Takeaways Explain This Topic AI

Area under a velocity-time graph is displacement, while the slope of that same graph is acceleration; on a distance-time graph the slope is speed.

Newton's third-law pair acts on two different bodies, which is why the two equal and opposite forces never cancel on a single free-body diagram.

Weight changes with location because W = mg, but mass does not: a 60 kg student weighs 588 N on Earth and 96 N on the Moon while staying 60 kg.

Work is zero whenever the force is perpendicular to the displacement, so carrying a bag horizontally at constant speed does no work on the bag.

Kinetic energy follows KE = 1/2 mv squared, so doubling speed quadruples kinetic energy and tripling it multiplies kinetic energy by nine.

Last updated: August 2026

8.1 Mechanics: Motion, Newton's Laws, Work, and Energy

Mechanics is the branch of physics that AdUCET science items draw on most heavily, because almost every question can be built from five or six formulas and finished with mental arithmetic. Adamson University publishes no content outline for AdUCET, so treat the topics below as standard Philippine Grade 11-12 General Physics 1 coverage rather than an official blueprint. Waves, heat, electricity and magnetism are handled separately in section 8.2.

Scalars, Vectors, and the Vocabulary of Motion

A scalar is fully described by a magnitude and a unit: 5 kg, 12 s, 40 m. A vector needs a magnitude and a direction: 40 m east, 9.8 m/s 2 ^2 2 downward. Most motion traps come from swapping one for the other.

Scalar Vector partner The difference that decides the answer

Distance ( d d d ) Displacement ( d ⃗ \vec{d} d ) Distance counts every metre travelled; displacement is only the straight line from start to finish

  • Speed Velocity Speed is distance over time; velocity is displacement over time and carries a direction
  • Mass Weight Mass is kilograms of matter; weight is the newtons of gravitational pull on that matter

Time, work, energy, power Force, acceleration, momentum The right-hand column reverses sign when the direction reverses

Worked orientation example. A student jogs 300 m north along Taft Avenue, turns around, and jogs 100 m south, taking 200 s in total.

Distance = 300 + 100 = 400 = 300 + 100 = 400 = 300 + 100 = 400 m; displacement = 300 − 100 = 200 = 300 - 100 = 200 = 300 − 100 = 200 m north.

Average speed = 400 ÷ 200 = 2 = 400 \div 200 = 2 = 400 ÷ 200 = 2 m/s.

Average velocity = 200 ÷ 200 = 1 = 200 \div 200 = 1 = 200 ÷ 200 = 1 m/s north.

Same trip, two different numbers. Acceleration is the rate of change of velocity, a = ( v f − v i ) / t a = (v_f - v_i)/t a = ( v f ​ − v i ​ ) / t , in m/s 2 ^2 2 ; an object accelerates when it speeds up, slows down, or merely changes direction.

The four kinematic equations

For uniform acceleration in a straight line, memorise which variable each equation leaves out and choose by elimination.

  • Equation Leaves out Choose it when the item gives you
  • v f = v i + a t v_f = v_i + at v f ​ = v i ​ + a t displacement initial speed, acceleration, time

d = v i t + 1 2 a t 2 d = v_i t + \tfrac{1}{2}at^2 d = v i ​ t + 2 1 ​ a t 2 final velocity initial speed, acceleration, time

v f 2 = v i 2 + 2 a d v_f^2 = v_i^2 + 2ad v f 2 ​ = v i 2 ​ + 2 a d time speeds and a distance, no clock

d = ( v i + v f 2 ) t d = \left(\dfrac{v_i + v_f}{2}\right)t d = ( 2 v i ​ + v f ​ ​ ) t acceleration both speeds and the time

For free fall , replace a a a with g = 9.8 g = 9.8 g = 9.8 m/s 2 ^2 2 (round to 10 10 10 for calculator-free work) and set v i = 0 v_i = 0 v i ​ = 0 for a dropped object. Mass is irrelevant: a one-peso coin and a bowling ball fall together when air resistance is negligible.

Worked example 1 — free fall from a building

A stone is dropped from the roof of a 45 m building. Using g = 10 g = 10 g = 10 m/s 2 ^2 2 :

Step 1. No final speed is given, so use d = 1 2 g t 2 d = \tfrac{1}{2}gt^2 d = 2 1 ​ g t 2 : 45 = 1 2 ( 10 ) t 2 = 5 t 2 45 = \tfrac{1}{2}(10)t^2 = 5t^2 45 = 2 1 ​ ( 10 ) t 2 = 5 t 2 .

Step 2. t 2 = 9 t^2 = 9 t 2 = 9 , so t = 3 t = 3 t = 3 s.

Step 3. v f = g t = 10 × 3 = 30 v_f = gt = 10 \times 3 = 30 v f ​ = g t = 10 × 3 = 30 m/s.

Check. v f 2 = 2 g d = 2 ( 10 ) ( 45 ) = 900 v_f^2 = 2gd = 2(10)(45) = 900 v f 2 ​ = 2 g d = 2 ( 10 ) ( 45 ) = 900 , and 900 = 30 \sqrt{900} = 30 900 ​ = 30 m/s. The two routes agree.

Reading motion graphs

Distance-time graph: the slope is speed. A horizontal line means at rest, a steeper line means faster, and a curving line means the speed is changing.

Velocity-time graph: the slope is acceleration, and the area under the line is the displacement . A line below the axis means motion in the reverse direction.

Worked example 2 — distance from a velocity-time graph

A tricycle accelerates uniformly from rest to 12 m/s in 4 s, cruises at 12 m/s for 6 s, then brakes uniformly to rest in 2 s. Break the area into three shapes:

  • Triangle: 1 2 ( 4 ) ( 12 ) = 24 \tfrac{1}{2}(4)(12) = 24 2 1 ​ ( 4 ) ( 12 ) = 24 m
  • Rectangle: 6 × 12 = 72 6 \times 12 = 72 6 × 12 = 72 m
  • Triangle: 1 2 ( 2 ) ( 12 ) = 12 \tfrac{1}{2}(2)(12) = 12 2 1 ​ ( 2 ) ( 12 ) = 12 m

Total displacement = 24 + 72 + 12 = 108 = 24 + 72 + 12 = 108 = 24 + 72 + 12 = 108 m.

Projectile motion

A projectile's horizontal and vertical motions are independent . Horizontal velocity stays constant (ignoring air resistance) while the vertical motion is ordinary free fall. Two consequences appear constantly in tests: a ball rolled off a table and a ball simply dropped from the same height hit the floor at the same time , and the flight path is a parabola whose range is greatest at a launch angle of 45 ∘ 45^\circ 4 5 ∘ .

Newton's Three Laws of Motion

First law (inertia). A body keeps its state of rest or of uniform straight-line motion unless a net external force acts. Inertia is measured by mass, which is why a loaded truck is harder to stop than a bicycle.

Second law. F n e t = m a F_{net} = ma F n e t ​ = ma . One newton is the force that gives 1 kg an acceleration of 1 m/s 2 ^2 2 . Acceleration always points in the direction of the net force, not of the largest single force.

Third law. If A pushes B, then B pushes A with equal magnitude in the opposite direction. The pair acts on two different bodies , so the two forces can never cancel on one free-body diagram.

The classic trap reads: if every force has an equal and opposite partner, how can anything accelerate? The answer is that the partner force is applied to the other object. When you push a cart, your push acts on the cart and the cart's push acts on you.

Mass, weight, and the normal force

Weight is a force: F g = m g F_g = mg F g ​ = m g . A 60 kg student weighs 60 × 9.8 = 588 60 \times 9.8 = 588 60 × 9.8 = 588 N on Earth, 60 × 1.6 = 96 60 \times 1.6 = 96 60 × 1.6 = 96 N on the Moon, and 60 × 3.7 = 222 60 \times 3.7 = 222 60 × 3.7 = 222 N on Mars, yet the mass stays 60 kg everywhere. The normal force ( N N N ) is the surface's perpendicular push back; on level ground with nothing else pressing down, N = m g N = mg N = m g .

Friction

Static friction holds a stationary object and grows to match whatever push you apply, up to a maximum f s = μ s N f_s = \mu_s N f s ​ = μ s ​ N . Kinetic friction , f k = μ k N f_k = \mu_k N f k ​ = μ k ​ N , is roughly constant once sliding starts, and μ s > μ k \mu_s > \mu_k μ s ​ > μ k ​ — which is exactly why a heavy aparador takes a hard shove to start moving and a gentler push to keep moving. Free-body diagram: crate pushed across a floor

  • N (normal, up)
  • ^
  • |
  • f_k <------- [ CRATE ] -------> F_applied
  • |
  • v
  • mg (weight, down)
  • Vertical: N = mg -> no vertical acceleration
  • Horizontal: F_net = F_applied - f_k -> a = F_net / m
  • Momentum, Impulse, and Collisions

Momentum is p = m v p = mv p = m v , in kg ⋅ \cdot ⋅ m/s, and it is a vector. Impulse is F Δ t = Δ p F\Delta t = \Delta p F Δ t = Δ p : spreading a collision over a longer contact time reduces the force, which is the whole design principle behind helmet padding, car crumple zones, and pulling your hands back as you catch a ball.

In a closed system, total momentum before a collision equals total momentum after. A 1,200 kg car moving at 15 m/s rear-ends a stationary 800 kg car and the two lock together: p = 1,200 × 15 = 18,000 p = 1{,}200 \times 15 = 18{,}000 p = 1 , 200 × 15 = 18 , 000 kg ⋅ \cdot ⋅ m/s, total mass = 2,000 = 2{,}000 = 2 , 000 kg, so the wreck moves off at 18,000 ÷ 2,000 = 9 18{,}000 \div 2{,}000 = 9 18 , 000 ÷ 2 , 000 = 9 m/s.

Work, Power, and Mechanical Energy

Work is W = F d cos ⁡ θ W = Fd\cos\theta W = F d cos θ , in joules . Work is zero in three situations: no displacement (straining against a concrete wall), force perpendicular to displacement ( cos ⁡ 90 ∘ = 0 \cos 90^\circ = 0 cos 9 0 ∘ = 0 , as when you carry a bag horizontally), or no force at all. Power is P = W / t P = W/t P = W / t , in watts ; 1 horsepower is about 746 W.

Kinetic energy: K E = 1 2 m v 2 KE = \tfrac{1}{2}mv^2 K E = 2 1 ​ m v 2 . Because speed is squared, doubling speed quadruples the kinetic energy — the reason stopping distances balloon.

Gravitational potential energy: P E = m g h PE = mgh PE = m g h , measured from whatever reference height you choose.

Conservation of mechanical energy: when only gravity does work, K E i + P E i = K E f + P E f KE_i + PE_i = KE_f + PE_f K E i ​ + P E i ​ = K E f ​ + P E f ​ .

Worked example 3 — power on a staircase

A 50 kg student runs up stairs 4 m high in 8 s, with g = 10 g = 10 g = 10 m/s 2 ^2 2 .

Work against gravity: W = m g h = 50 × 10 × 4 = 2,000 W = mgh = 50 \times 10 \times 4 = 2{,}000 W = m g h = 50 × 10 × 4 = 2 , 000 J.

Power: P = W / t = 2,000 ÷ 8 = 250 P = W/t = 2{,}000 \div 8 = 250 P = W / t = 2 , 000 ÷ 8 = 250 W.

Worked example 4 — energy conservation on a falling mango

A 3 kg mango drops from a branch 5 m up, with g = 10 g = 10 g = 10 m/s 2 ^2 2 .

At the top: P E = 3 × 10 × 5 = 150 PE = 3 \times 10 \times 5 = 150 PE = 3 × 10 × 5 = 150 J and K E = 0 KE = 0 K E = 0 .

Just before impact: P E = 0 PE = 0 PE = 0 , so K E = 150 KE = 150 K E = 150 J.

Solve for speed: 1 2 ( 3 ) v 2 = 150 ⇒ v 2 = 100 ⇒ v = 10 \tfrac{1}{2}(3)v^2 = 150 \Rightarrow v^2 = 100 \Rightarrow v = 10 2 1 ​ ( 3 ) v 2 = 150 ⇒ v 2 = 100 ⇒ v = 10 m/s.

Halfway down (2.5 m): P E = 75 PE = 75 PE = 75 J and K E = 75 KE = 75 K E = 75 J — the total is still 150 J.

Simple Machines and Mechanical Advantage

Mechanical advantage is M A = load force ÷ effort force MA = \text{load force} \div \text{effort force} M A = load force ÷ effort force ; the ideal mechanical advantage is I M A = effort distance ÷ load distance IMA = \text{effort distance} \div \text{load distance} I M A = effort distance ÷ load distance . A machine multiplies force, never energy: ideally work in equals work out, and real machines lose part of the input to friction, so efficiency = ( W o u t / W i n ) × 100 % = (W_{out}/W_{in}) \times 100\% = ( W o u t ​ / W in ​ ) × 100% is always below 100%.

Lever: $MA = $ effort arm ÷ \div ÷ load arm. First class has the fulcrum in the middle (seesaw, scissors), second class has the load in the middle (wheelbarrow, nutcracker), third class has the effort in the middle (tongs, fishing rod, the human forearm) and trades force for speed with M A < 1 MA < 1 M A < 1 .

Pulley: a fixed pulley has M A = 1 MA = 1 M A = 1 and only redirects the effort; a movable pulley gives M A = 2 MA = 2 M A = 2 ; a block and tackle gives M A MA M A equal to the number of rope strands supporting the load.

Inclined plane: I M A = slope length ÷ height IMA = \text{slope length} \div \text{height} I M A = slope length ÷ height . A 6 m ramp rising 1.5 m has I M A = 6 ÷ 1.5 = 4 IMA = 6 \div 1.5 = 4 I M A = 6 ÷ 1.5 = 4 , so a 200 N crate ideally needs only 200 ÷ 4 = 50 200 \div 4 = 50 200 ÷ 4 = 50 N of push. Energy still balances: 200 × 1.5 = 300 200 \times 1.5 = 300 200 × 1.5 = 300 J lifted, 50 × 6 = 300 50 \times 6 = 300 50 × 6 = 300 J pushed.

What Examiners Test

Distance versus displacement in a there-and-back trip — the classic zero-displacement item.

Whether you read slope or area off a graph. Area under a velocity-time line is displacement; slope of a distance-time line is speed.

Mass unchanged, weight changed, when an object is moved to the Moon or Mars.

Third-law pairs, testing whether you know the two forces act on different bodies.

Zero-work situations, especially carrying a load horizontally at constant speed.

The squared term in K E = 1 2 m v 2 KE = \tfrac{1}{2}mv^2 K E = 2 1 ​ m v 2 — tripling the speed multiplies kinetic energy by nine, not by three.