LET Elementary Physics — Motion, Forces and Newton's LawsSummary

Distance is the total length of the path traveled—always a scalar (magnitude only), always positive. Displacement is the straight-line change in position from start to finish, including direction—a vector. Example: A pupil walks 3 meters east, then 4 meters north. Distance = 3 + 4 = 7 m. Displacement = √(3² + 4²) = 5 m, directed northeast. This 3–4–5 triangle is a favorite LET setup. Key insight: If an object returns to its starting point, displacement is zero even though distance is not—like a runner completing one lap of the oval.

Speed = distance ÷ time (scalar, m/s). Velocity = displacement ÷ time (vector, m/s). Acceleration = (final velocity − initial velocity) ÷ time (m/s²). Example: A jeepney travels 60 km in 1.5 hours; average speed = 60 ÷ 1.5 = 40 km/h. If the jeepney heads north at 40 km/h, its velocity is 40 km/h north. A car accelerating from 0 to 20 m/s in 5 seconds has a = (20 − 0) ÷ 5 = 4 m/s². Deceleration is negative acceleration: a tricycle slowing from 12 m/s to 0 in 4 seconds has a = (0 − 12) ÷ 4 = −3 m/s². Constant velocity = zero acceleration, even if direction changes (a car rounding a curve at constant speed is still accelerating).

When acceleration is constant, three equations connect motion variables (u = initial velocity, v = final velocity, a = acceleration, t = time, d = displacement): (1) v = u + at; (2) d = ut + ½at²; (3) v² = u² + 2ad. Worked example (Eq. 1): Object moving at 2 m/s accelerates at 3 m/s² for 4 seconds; v = 2 + (3)(4) = 14 m/s. Worked example (Eq. 2): Car starts from rest, accelerates at 2 m/s² for 5 seconds; d = 0 + ½(2)(5²) = 25 m. These three equations cover all LET motion scenarios.

Near Earth's surface, gravity pulls all objects downward with acceleration g ≈ 9.8 m/s² (often rounded to 10 m/s² for estimates). In free fall (ignoring air resistance), a heavy stone and a light feather fall at the same rate because acceleration does not depend on mass. Free-fall equations use g in place of a, with u = 0 for dropped objects. Worked example: Stone dropped from a bridge; after 3 seconds, speed = gt = (9.8)(3) = 29.4 m/s. Distance fallen = ½gt² = ½(9.8)(3²) = 44.1 m. In a vacuum, a feather and coin fall together at the same rate; in real air, the feather falls slower only because of air resistance, not gravity.

A force is a push or pull, measured in newtons (N). Forces are vectors (direction matters). When several forces act on an object, they combine into a net force (resultant). Same direction → add; opposite direction → subtract. When net force = 0, the object is in equilibrium (at rest or moving at constant velocity). Common forces: gravity/weight (downward), normal force (surface pushing up), friction (opposes sliding), tension (in ropes), applied force. Worked example: Box pushed forward with 50 N; friction resists with 20 N. Net force = 50 − 20 = 30 N forward.

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force. Inertia is the tendency to resist changes in motion; it increases with mass. A heavier object has more inertia and resists acceleration more. Real-world example: Passengers lurch forward when a jeepney brakes—their bodies tend to continue forward because of inertia. This is why seatbelts are essential. No net force → no acceleration → constant velocity (or rest).

Acceleration of an object is directly proportional to net force and inversely proportional to mass: F = ma (net force in newtons = mass in kg × acceleration in m/s²). Rearranged: a = F/m. Worked example: Net force of 20 N on 10 kg cart; a = 20 ÷ 10 = 2 m/s². Doubling the force doubles acceleration; doubling the mass halves acceleration. Weight (a special case): W = mg. A 5 kg bag weighs W = (5)(9.8) = 49 N. Mass (kg) is constant everywhere; weight (newtons, a force) changes with gravity. The same bag weighs less on the Moon.

For every action, there is an equal and opposite reaction. Forces come in pairs, but they act on different objects. When you push a wall, the wall pushes back on you with equal force. A rocket rises because it pushes gas down; the gas pushes the rocket up. A swimmer moves forward by pushing water backward. A bird pushes air down; the air pushes the bird up. Action-reaction pairs never cancel each other because they act on different bodies. If they acted on the same body, the object could not accelerate—but it does, because the forces are on different objects.

A free-body diagram shows all forces acting on a single object as arrows (vectors), with proper direction and length representing magnitude. Example: A book resting on a table has gravity (weight) pulling down and normal force pushing up; if equal, net force = 0, object at rest (equilibrium). If someone pushes the book, the applied force must exceed friction for acceleration to occur. Free-body diagrams help visualize which forces are balanced and which are unbalanced, directly predicting whether an object will accelerate or stay in equilibrium.

Momentum (p) = mass × velocity (kg·m/s); it measures 'quantity of motion.' A 1000 kg car at 20 m/s has p = (1000)(20) = 20,000 kg·m/s; a heavy truck at the same speed has far greater momentum and is harder to stop. Impulse = force × time (N·s), and impulse = change in momentum. Why car airbags save lives: they lengthen stopping time, reducing force for the same momentum change. Conservation of momentum: in a collision with no outside forces, total momentum before = total momentum after. Two ice skaters pushing off each other have zero total momentum before; they glide apart in opposite directions, still with zero total momentum.

A simple machine makes work easier by changing the size or direction of force. Mechanical advantage (MA) ≈ how many times the machine multiplies effort. Machines trade a smaller force over a longer distance for a larger force over a shorter distance; they do not create energy. Six simple machines: (1) Lever (seesaw, crowbar, scissors): MA = effort arm ÷ load arm. Example: Effort arm 3 m, load arm 1 m; MA = 3. A 100 N effort lifts 300 N. (2) Inclined plane (ramp): MA = length ÷ height. Example: Ramp 4 m long, 1 m high; MA = 4. (3) Wedge (knife, axe, chisel): two inclined planes. (4) Screw (jar lid, bolt): inclined plane in spiral. (5) Pulley (flagpole, crane): changes direction; multiple pulleys multiply force. (6) Wheel and axle (doorknob, steering wheel): multiplies force or distance in rotation. Three lever classes: first-class (fulcrum in middle, like seesaw), second-class (load in middle, like wheelbarrow), third-class (effort in middle, like tongs).

Distance and displacement are foundational measurements of position change. Speed and velocity build directly on these: speed = distance ÷ time; velocity = displacement ÷ time. Both are rates of change, but velocity carries directional information, making it a vector.

Acceleration measures how quickly velocity changes. If velocity is constant, acceleration is zero. Acceleration can involve change in speed, change in direction, or both. This relationship is central to understanding motion.

Newton's second law directly connects acceleration to force: acceleration results from net force divided by mass. A larger net force produces larger acceleration; a larger mass resists acceleration. This is the quantitative form of the first law.

Newton's first law describes inertia as the resistance to motion change. Inertia increases with mass. A more massive object requires a larger force to produce the same acceleration. This relationship explains why a full shopping cart is harder to push than an empty one.

When two objects collide (action-reaction), their momenta change in equal and opposite ways. Impulse (force × time) governs how much momentum changes. Understanding that forces come in pairs helps explain why both colliding objects are affected.

Free-body diagrams visually represent all forces acting on an object. When all forces balance, the net force is zero and the object is in equilibrium. Unbalanced forces (net force ≠ 0) cause acceleration. The diagram is a tool for predicting motion.

Simple machines use the principle that a smaller force applied over a longer distance can do the same work as a larger force over a shorter distance. Mechanical advantage quantifies this trade-off. All six simple machines exploit this principle.

Simple machines are applications of Newton's laws. A lever (first-class) is in equilibrium when the effort and load produce equal torques. Mechanical advantage allows us to lift heavy objects (second law: F = ma) without superhuman strength (third law: the object pushes back, but the lever redistributes forces).