LET Elementary Physics — Motion, Forces and Newton's LawsRevision Notes

Formulas

Exam Tips

• Whenever a problem describes movement in two perpendicular directions, immediately think 'Pythagorean theorem' for displacement.
• If the problem says the object returns to the start, displacement = 0. This is an almost guaranteed LET trick item.
• The LET often uses the 3-4-5, 5-12-13, or 8-15-17 Pythagorean triples to make calculations fast — recognize these patterns.
• Read carefully: 'how far did it travel?' usually means distance; 'how far is it from the start?' usually means displacement.

Key Points

• All quantities in mechanics are either scalars (magnitude only) or vectors (magnitude AND direction). This distinction is the starting point for everything else in the chapter.
• Distance is the total length of the path an object travels. It is always positive and is a scalar quantity.
• Displacement is the straight-line change in position from start to finish, including direction. It is a vector quantity and can be zero even when distance is not.
• Classic LET setup — the 3-4-5 triangle: A pupil walks 3 m east, then 4 m north. Distance = 3 + 4 = 7 m. Displacement = √(3² + 4²) = √25 = 5 m, directed northeast.
• If an object returns to its starting point, displacement = 0 m regardless of distance covered. A runner completing one full oval lap has real distance but zero displacement.
• In the K-12 Grade 3 Science curriculum, pupils begin to distinguish between position and movement, making this concept a direct teaching competency for you.

Definitions

Section Title

1. Describing Motion: Distance, Displacement, and the Scalar-Vector Distinction

Common Mistakes

• Confusing distance and displacement: remember that distance is the full path length while displacement is the shortest straight-line route from start to end.
• Forgetting that displacement can be zero. A pupil who walks around a rectangular classroom and returns to her seat has a displacement of zero.
• Adding perpendicular displacements directly (e.g., saying 3 m + 4 m = 7 m displacement) instead of using the Pythagorean theorem to get 5 m.
• Treating speed and velocity as the same thing — speed is scalar (magnitude only), velocity is vector (magnitude + direction).

Formulas

Exam Tips

• Constant velocity → zero acceleration. Changing velocity (speed or direction) → nonzero acceleration. Memorize this rule.
• If the LET asks about a car going around a circular track at constant speed, the answer regarding acceleration is NOT zero — direction is changing, so velocity is changing.
• Unit conversion shortcut: 1 m/s = 3.6 km/h. So 40 km/h = 40 ÷ 3.6 ≈ 11.1 m/s.
• LET problems on acceleration often give you initial and final speeds and time — go straight to a = (v – u) / t.

Key Points

• Speed = distance ÷ time (scalar). Velocity = displacement ÷ time (vector). These two are numerically equal only when the object moves in a straight line without reversing.
• Average speed uses total distance; average velocity uses total displacement.
• Acceleration is the rate of change of velocity: a = (v – u) / t, where u is initial velocity and v is final velocity. It is a vector.
• An object can have zero acceleration even while moving — as long as velocity is constant (same speed and same direction).
• An object can be accelerating even at constant speed if its direction changes (e.g., a car turning a corner). This is a conceptual LET favorite.
• Deceleration is negative acceleration — the object is slowing down. A tricycle braking from 12 m/s to rest in 4 s has a = (0 – 12) / 4 = –3 m/s².
• SI unit of speed and velocity: meters per second (m/s). SI unit of acceleration: meters per second squared (m/s²).

Definitions

Section Title

2. Speed, Velocity, and Acceleration

Common Mistakes

• Using distance instead of displacement when computing velocity — this gives speed, not velocity.
• Assuming constant speed means zero acceleration. Remember: if direction changes, acceleration is present even at constant speed.
• Forgetting the sign of acceleration: slowing down means negative acceleration (deceleration), not zero acceleration.
• Mixing up units (km/h vs. m/s). To convert: multiply km/h by 1000/3600, or divide by 3.6, to get m/s.

Formulas

Exam Tips

• Memorize the three equations in order: (1) v = u + at, (2) d = ut + ½at², (3) v² = u² + 2ad. Practice identifying which variable is missing to select the right equation.
• If 'starts from rest' appears in the problem, set u = 0. This simplifies all three equations immediately.
• If 'comes to rest' appears, set v = 0. Then solve for whatever the problem asks.
• For free fall from rest: d = ½(9.8)t² ≈ ½(10)t² = 5t² (using g ≈ 10 for quick mental math). After 3 s: d = 5(9) = 45 m.

Key Points

• These three equations apply ONLY when acceleration is constant (uniform). They connect the five variables: u (initial velocity), v (final velocity), a (acceleration), t (time), and d (displacement).
• Equation 1: v = u + at — Use when you know u, a, t and need v.
• Equation 2: d = ut + ½at² — Use when you know u, a, t and need d (displacement).
• Equation 3: v² = u² + 2ad — Use when time is NOT given but you know displacement.
• For a dropped object (free fall from rest): u = 0, so Equation 2 simplifies to d = ½gt² and Equation 1 simplifies to v = gt.
• These equations are the engine of most LET kinematics calculation items. Identifying which equation to use is the key skill.
• Always list what you know and what you need before selecting an equation — this prevents formula selection errors under exam pressure.

Definitions

Section Title

3. Equations of Uniformly Accelerated Motion (UAM)

Common Mistakes

• Using u when you should use v or vice versa — always label initial vs. final clearly before substituting.
• Forgetting to square t in the term ½at² — this is the most frequent arithmetic error in displacement calculations.
• Applying UAM equations when acceleration is NOT constant (e.g., a car in stop-and-go traffic). These equations require uniform/constant acceleration.
• Confusing displacement (d) with total distance when the object reverses direction — the equations give displacement (vector), not necessarily the total path length.

Formulas

Exam Tips

• When an object is on a flat surface at rest: Normal force = Weight. This is your starting point for flat-surface problems.
• Equilibrium does NOT mean the object is stationary — a tricycle moving at constant speed on a flat road is in equilibrium (driving force = friction).
• Mass vs. weight: mass is the same everywhere (kg), weight changes with gravity (N). The LET tests this distinction with Moon/space scenarios.
• For LET problems involving a box on a flat surface with friction, net force = applied force – friction. If net force > 0, the object accelerates.

Key Points

• A force is a push or a pull measured in newtons (N). Forces are vectors — direction always matters.
• Net force (resultant force) is the vector sum of all forces acting on an object. When forces act along the same line, add same-direction forces and subtract opposing forces.
• When net force = 0, the object is in equilibrium: it is either at rest or moving at constant velocity (connects directly to Newton's First Law).
• Key forces in the LET: Weight/gravity (W = mg, downward), Normal force (surface pushes perpendicular to surface, upward on flat ground), Friction (opposes motion, horizontal), Tension (along a string or rope), Applied force.
• A book on a table: weight pulls it down, normal force pushes it up — they are equal and opposite, net force = 0, so the book is in equilibrium.
• Free-body diagrams (FBDs) are the tool for analyzing forces. Draw all forces as arrows on a single object, then compute the net force.
• The LET sometimes shows a scenario and asks whether an object is in equilibrium — check if all forces cancel.

Definitions

Section Title

4. Force, Net Force, and Equilibrium

Common Mistakes

• Treating weight and mass as the same thing. Weight (W = mg) is a force in newtons; mass is the amount of matter in kilograms.
• Adding forces without considering direction. Forces in opposite directions must be subtracted, not added.
• Confusing 'balanced forces' (equilibrium, net force = 0) with 'no forces' (no forces at all). Both produce zero acceleration but are different situations.
• Including forces on other objects in a free-body diagram. An FBD shows ONLY the forces acting ON the single object being analyzed.

Formulas

Exam Tips

• Memorize the three laws in sequence: 1st = Inertia (tendency to resist change), 2nd = F = ma (force causes acceleration), 3rd = Equal and opposite reaction on a DIFFERENT object.
• For any 'why does the passenger lurch?' or 'why does the car skid?' question, the answer involves Newton's First Law (inertia).
• For any 'calculate the acceleration' or 'calculate the force' question, go directly to F = ma.
• The LET tests Third Law with rockets, birds, swimming, walking, and gun recoil. In ALL cases, identify the two different objects that the action and reaction act upon.
• Seatbelts, airbags, and crash helmets are First Law/inertia safety devices — expect these to appear in context-based LET items.

Key Points

• FIRST LAW (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless a net external force acts on it. This is the 'default state' principle.
• Inertia is the tendency to resist changes in motion. Greater mass = greater inertia. A loaded truck is harder to start and stop than a bicycle because it has more inertia.
• Philippine classroom example of First Law: Passengers in a jeepney lurch forward when the driver brakes suddenly — their bodies' inertia keeps them moving forward while the jeepney stops.
• SECOND LAW (Law of Acceleration): Net force = mass × acceleration (F = ma). A larger force produces greater acceleration; a larger mass produces less acceleration for the same force.
• Second Law is the mathematical heart of mechanics. All numerical LET force problems use F = ma in some form.
• THIRD LAW (Law of Action-Reaction): For every action force, there is an equal and opposite reaction force acting on a DIFFERENT object. Forces always come in pairs on different bodies.
• Key Third Law examples: rocket propulsion (gas pushed down, rocket pushed up), swimmer (pushes water back, water pushes swimmer forward), bird (pushes air down, air pushes bird up).
• Action-reaction pairs do NOT cancel because they act on different objects. This is the most misunderstood aspect of the Third Law.

Definitions

Section Title

5. Newton's Three Laws of Motion

Common Mistakes

• Confusing the First Law with the idea that 'objects slow down on their own.' Objects in motion stay in motion; friction is a force that slows them, not a natural tendency.
• In Second Law problems, using total applied force instead of NET force. You must subtract friction and other opposing forces before applying F = ma.
• Thinking action-reaction pairs cancel each other out. They cannot cancel because they act on DIFFERENT objects, not the same object.
• Assuming heavier objects fall faster — Newton's Second Law combined with gravity shows that a = W/m = mg/m = g, which is the same for all masses. In a vacuum, all objects fall at the same rate.

Formulas

Exam Tips

• Memorize: Large mass or large velocity → large momentum. A slow truck has more momentum than a fast motorcycle.
• For airbag/helmet/padded flooring questions: longer time → smaller force for the same impulse. This is the safety principle the LET tests.
• Conservation of momentum in collisions: total p before = total p after. For a 'push-off' from rest, the two resulting momenta are equal and opposite.
• Unit check: Force (N) × time (s) = N·s = kg·m/s² × s = kg·m/s = momentum unit. This confirms Impulse = Δp.

Key Points

• Momentum (p) is the product of mass and velocity. It measures the 'quantity of motion' an object has. Unit: kg·m/s.
• A heavy object moving fast has large momentum; a light object moving slowly has small momentum. A slow-moving truck can have MORE momentum than a fast-moving bicycle because of its large mass.
• Impulse = Force × time. Impulse equals the change in momentum (Impulse-Momentum Theorem).
• Safety application of impulse: Airbags and crash helmets increase the time of impact (t), which reduces the force experienced for the same change in momentum. This is why they save lives.
• Conservation of momentum: In a closed system with no external forces, total momentum before a collision = total momentum after a collision.
• Example of conservation: Two ice skaters at rest push each other — total initial momentum = 0. After pushing, they move in opposite directions with equal and opposite momenta, so total final momentum = 0.
• The LET tests both the formula and the conceptual application of momentum conservation in collisions and explosions.

Definitions

Section Title

6. Momentum and Impulse

Common Mistakes

• Confusing momentum with force. Momentum is mass times velocity; force is mass times acceleration. They are related but different.
• Forgetting that momentum is a vector — direction matters in conservation problems. Two objects moving in opposite directions can have a total momentum of zero.
• Not applying the conservation of momentum principle when external forces are negligible, leading to unnecessary complexity in collision problems.
• Mixing up impulse (N·s) with momentum (kg·m/s) — these have the same units and are equal to each other (Δp = F·t), but they represent different physical ideas.

Formulas

Exam Tips

• Know the six simple machines and one clear Philippine example for each: Lever (palo-sombrero/crowbar), Inclined plane (ramp/driveway), Wedge (bolo/chisel), Screw (turnilyo), Pulley (well/haligi), Wheel and axle (gripo/doorknob).
• For lever class identification: Find the fulcrum first, then determine what is in the middle — fulcrum in middle = 1st class, load in middle = 2nd class, effort in middle = 3rd class.
• The human body uses third-class levers extensively (forearm, jaw). The LET tests this biology-physics connection.
• When calculating MA from an inclined plane: MA = ramp length ÷ ramp height (NOT the horizontal distance).
• Work = Force × Distance. If MA = 4, the effort force is ¼ of the load but must be applied over 4× the distance. Total work remains the same.

Key Points

• A simple machine makes work easier by changing the size or direction of a force. It does NOT create energy — it trades force for distance.
• Mechanical Advantage (MA) tells how many times a machine multiplies the effort force. MA = Load Force ÷ Effort Force = Effort Arm ÷ Load Arm (for levers) = Length ÷ Height (for inclined planes).
• The six simple machines: Lever, Inclined Plane, Wedge, Screw, Pulley, Wheel and Axle. Know each one's everyday Philippine example.
• Three classes of levers differ by the position of the fulcrum (F), effort (E), and load (L): 1st class = FEL (fulcrum in middle, e.g., seesaw, crowbar), 2nd class = EFL (load in middle, e.g., wheelbarrow, bottle opener), 3rd class = ELF (effort in middle, e.g., tongs, broom, human forearm).
• Key principle: A machine with higher MA requires less force but the effort must move a greater distance. Work input = Work output (in an ideal, frictionless machine).
• Lever MA worked example: Effort arm = 3 m, load arm = 1 m. MA = 3 ÷ 1 = 3. A 100 N effort lifts a 300 N load.
• Inclined plane MA worked example: Ramp length = 4 m, height = 1 m. MA = 4 ÷ 1 = 4. Pushing a load up the ramp needs only ¼ the force of lifting it straight up, but over 4× the distance.
• In the K-12 curriculum, simple machines are taught in Grade 4 Science. As a future teacher, understanding both the concepts and the teaching approach is important.

Definitions

Section Title

7. Simple Machines and Mechanical Advantage

Common Mistakes

• Thinking simple machines create energy or reduce the total work done. They only redistribute force and distance — work in always equals work out (ideal case).
• Confusing lever classes: Remember the pattern FEL (1st), LFE read as load-middle (2nd), ELF read as effort-middle (3rd). A seesaw is 1st class; a wheelbarrow is 2nd class; tongs are 3rd class.
• Using Length/Height for a lever or Effort/Load for an inclined plane — each machine has its own MA formula. Match the formula to the machine.
• Assuming higher MA is always better — a machine with high MA moves the load only a small distance for each large distance of effort movement.