Apply motion, force, and Newton's Laws. - GED Science

SECTION 1

Historical Context & Motivation

For thousands of years, people believed that objects only move when a force actively pushes or pulls them — and that the natural state of any object is to be at rest. The ancient Greek philosopher Aristotle taught that heavier objects fall faster and that motion requires a continuous cause. These ideas went mostly unchallenged for nearly two thousand years, until a wave of careful experiments and mathematical reasoning overturned them.

~350 BC • Aristotle's Physics

Aristotle argued that objects move only when a force is applied and that heavier objects fall faster. These ideas dominated Western science for centuries.

1589 • Galileo's Experiments

Galileo Galilei demonstrated that all objects fall at the same rate regardless of mass (ignoring air resistance) and introduced the concept of inertia — the tendency of an object to resist changes in its motion.

1687 • Newton's Principia

Isaac Newton published the Principia Mathematica, laying out his three laws of motion and the law of universal gravitation. These laws unified terrestrial and celestial mechanics.

1905 • Einstein's Relativity

Albert Einstein refined Newton's laws for objects moving near the speed of light. For everyday speeds, however, Newton's laws remain accurate and are still used in engineering and science today.

Newton's three laws of motion answer a fundamental question: what causes objects to move, stop, or change direction? Whether you are driving a car, catching a ball, or launching a rocket, these same laws govern every motion you observe. On the GED Science test, you will be asked to interpret scenarios, read graphs, and analyze data that all connect back to these core principles.

SECTION 2

Core Principles & Definitions

Before diving into Newton's three laws, you need a solid grasp of the key terms. Motion, force, and mass are the building blocks of classical mechanics. Each term has a precise scientific meaning that may differ slightly from how we use these words in everyday conversation.

Motion & Velocity

Motion is any change in an object's position over time. Speed measures how fast an object moves, while velocity includes both speed and direction (e.g., 60 km/h north).

Acceleration

Acceleration is the rate at which velocity changes. An object accelerates whenever it speeds up, slows down, or changes direction. Measured in meters per second squared (m/s²).

Force

A force is a push or pull on an object. Forces are measured in newtons (N). Common forces include gravity, friction, and applied (push/pull) forces.

Mass vs. Weight

Mass is the amount of matter in an object (measured in kilograms). Weight is the gravitational force on that mass (measured in newtons). Your mass stays the same on Earth or the Moon; your weight does not.

Net Force

The net force is the overall force acting on an object after all individual forces are combined. If forces are balanced (net force = 0), the object's motion does not change.

✦

KEY TAKEAWAY

Think of a hockey puck on smooth ice. Once you flick it, it glides in a straight line at a constant speed because the ice provides almost no friction. The puck doesn't need a continuous push to keep moving — it needs a force only to change its speed or direction. That insight — that motion itself is natural and doesn't need a cause — is the heart of Newton's First Law.

SECTION 3

Newton's Three Laws — Visual Overview

This diagram shows each of Newton's three laws with a visual example. The bottom section illustrates balanced forces (no acceleration), unbalanced forces (acceleration occurs), and friction as an opposing force.

The diagram above summarizes three key ideas. Newton's First Law (left panel) tells us that an object at rest stays at rest, and an object in motion stays in motion at constant speed in a straight line, unless an unbalanced force acts on it. Newton's Second Law (center panel) quantifies the relationship: the acceleration of an object equals the net force divided by its mass. Newton's Third Law (right panel) states that for every action force, there is an equal and opposite reaction force. The bottom panels show how balanced and unbalanced forces determine whether an object accelerates.

SECTION 4

Mathematical Framework

Newton's Second Law gives us the central equation for motion and force. On the GED, you may need to rearrange this equation or plug in values from a data table. Let's also look at two related formulas: speed and weight.

NEWTON'S SECOND LAW

F = m × a

F = net force (in newtons, N) • m = mass (in kilograms, kg) • a = acceleration (in m/s²). This can be rearranged: a = F ÷ m, or m = F ÷ a.

SPEED

speed = distance ÷ time

Speed measures how far an object travels in a given amount of time. Common units include meters per second (m/s) or kilometers per hour (km/h).

WEIGHT

W = m × g

W = weight (in newtons) • m = mass (in kg) • g = acceleration due to gravity (≈ 9.8 m/s² on Earth). Weight is simply the force of gravity pulling on mass.

ACCELERATION

a = (v_final − v_initial) ÷ time

Acceleration is the change in velocity divided by the time over which the change occurs. A negative acceleration (deceleration) means the object is slowing down.

💡

GED TIP

On the GED Science test, you are not expected to memorize formulas from scratch. Equations are often provided in the stimulus (the passage or data you read before answering). Your job is to understand what each variable means and how to plug in the given numbers. Practice rearranging F = m × a into its three forms so you feel comfortable no matter which variable the question asks you to find.

SECTION 5

Types of Forces & Free-Body Diagrams

In everyday life, multiple forces often act on an object at the same time. A free-body diagram is a simple sketch that shows an object as a dot or box and uses arrows to represent every force acting on it. The length of each arrow represents the magnitude (strength) of the force, and the direction of the arrow shows which way the force pushes or pulls.

A free-body diagram for a 10 kg box on a flat surface. Four forces act on the box: gravity pulling down, the normal force pushing up, an applied force pushing right, and friction opposing motion to the left. The vertical forces are balanced, but the horizontal forces are unbalanced, producing a net force of 25 N to the right.

In the free-body diagram above, the vertical forces (gravity pulling down at 98 N and the normal force pushing up at 98 N) cancel each other out, so the box does not accelerate vertically. Horizontally, the applied force (40 N right) is greater than friction (15 N left), giving a net force of 25 N to the right. Using Newton's Second Law, we can calculate the acceleration: a = F ÷ m = 25 N ÷ 10 kg = 2.5 m/s². The box accelerates to the right.

Force Type	Description	Example
Gravity	Pulls objects toward the center of Earth (or any massive body)	A ball falling from a table
Normal Force	Support force perpendicular to a surface, pushing back against the object's weight	A book resting on a desk
Friction	Opposes the direction of sliding or attempted sliding between surfaces	Brakes slowing a car
Applied Force	A push or pull exerted by a person or object	Pushing a shopping cart
Tension	Pulling force transmitted through a rope, cable, or string	Towing a car with a chain
Air Resistance	A form of friction caused by air molecules pushing against a moving object	A parachute slowing a skydiver

Common Types of Forces

SECTION 6

Worked Example

Let's walk through a GED-style problem step by step. Pay attention to how we identify the given information, select the right equation, and solve.

Calculating Acceleration from Force and Mass

1
Step 1 — Read the Problem

A warehouse worker pushes a 50 kg crate across a concrete floor with a steady force of 200 N. Friction between the crate and the floor is 75 N. What is the crate's acceleration?
2
Step 2 — Identify Given Values

Mass (m) = 50 kg. Applied force = 200 N (forward). Friction = 75 N (backward, opposing motion). We need to find acceleration (a).
3
Step 3 — Find the Net Force

Net force = Applied force − Friction = 200 N − 75 N

Net force = 125 N (forward)
4
Step 4 — Apply Newton's Second Law

F = m × a, so rearranging for acceleration: a = F ÷ m = 125 N ÷ 50 kg

a = 2.5 m/s²
5
Step 5 — Interpret the Answer

The crate accelerates at 2.5 m/s² in the forward direction. This means every second, its velocity increases by 2.5 meters per second. If friction were larger, acceleration would be smaller. If the worker pushed harder, acceleration would be larger.

🔑

PROBLEM-SOLVING STRATEGY

Always start by finding the net force first. Add forces in the same direction; subtract forces that oppose each other. Only after you know the net force should you use F = m × a. Think of it like calculating your take-home pay: you need to subtract deductions (friction, opposing forces) from your gross pay (applied force) before you know what you actually receive (net force that produces acceleration).

SECTION 7

Common Misconceptions vs. Correct Physics

Newton's laws are intuitive once you understand them, but everyday experience can trick you into believing ideas that are actually incorrect. The GED Science test often includes answer choices based on these misconceptions, so knowing them is a powerful test-taking strategy.

Common Misconception	Correct Understanding
"Objects need a constant force to keep moving."	Objects in motion stay in motion without any force (1st Law). A force is only needed to overcome friction or change velocity.
"Heavier objects fall faster than lighter ones."	All objects accelerate at the same rate due to gravity (9.8 m/s²) in the absence of air resistance. A feather and a hammer fall together in a vacuum.
"If an object is at rest, no forces are acting on it."	Multiple forces can act on a stationary object — they just cancel out (balanced forces). A book on a table has gravity pulling it down and the normal force pushing it up.
"Action-reaction forces cancel each other out."	Action-reaction pairs act on DIFFERENT objects, so they cannot cancel. When you push a wall, the wall pushes you back — but one force is on you, the other is on the wall.
"A faster object has more force."	Speed is not a force. A moving object has momentum (mass × velocity) but may have zero net force acting on it if it moves at constant velocity.

Misconceptions That Appear as GED Distractors

⚠️

TEST STRATEGY

When you see a GED question about force and motion, look at the answer choices before doing calculations. One or two wrong choices will almost always match a common misconception listed above. Eliminating those immediately improves your odds, even if you're unsure about the math.

SECTION 8

Newton's Laws and Advanced Concepts

Newton's laws are the foundation for most of physics, but they connect to concepts you may encounter on the GED or in further study. Momentum is the product of mass and velocity (p = m × v). Newton's Second Law can also be expressed as: force equals the rate of change of momentum. The concept of momentum helps explain collisions, car safety features like airbags, and why it's harder to stop a moving truck than a bicycle.

Newton's Classical Mechanics	Advanced Physics
Works perfectly for everyday speeds and sizes	Einstein's relativity is needed for speeds near the speed of light
Force causes acceleration (F = ma)	Quantum mechanics describes forces at the subatomic scale
Gravity is a force that pulls masses together	General relativity describes gravity as a curvature of spacetime
Mass is constant and does not change with speed	Relativistic mass increases as an object approaches the speed of light

Newton vs. Advanced Physics — When Each Applies

For the GED Science test, you only need Newton's classical mechanics. These laws accurately describe virtually every situation you'll encounter on the exam — from car crashes to rocket launches to simple machines. Understanding F = m × a and the three laws gives you a powerful toolkit for answering physical science questions.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

A passenger in a car is wearing a seatbelt. The car suddenly stops, but the passenger's body lurches forward against the seatbelt. Which of Newton's laws best explains why the passenger's body continues to move forward even though the car has stopped?

A. Newton's First Law (Inertia) — an object in motion tends to stay in motion unless acted upon by an unbalanced force.
B. Newton's Second Law — the force of the brakes causes the passenger to accelerate forward.
C. Newton's Third Law — the car pushes backward on the road, and the road pushes forward on the passenger.
D. The law of gravity — gravity pulls the passenger forward in the car.

Show answer (A)

The correct answer is A. Newton's First Law (the law of inertia) explains that an object in motion stays in motion at the same speed and direction unless an external unbalanced force acts on it. When the car stops suddenly, the passenger's body continues moving forward because it resists the change in motion. The seatbelt provides the unbalanced force that eventually stops the passenger. Choice B is incorrect because Newton's Second Law describes the relationship between force, mass, and acceleration — the brakes act on the car, not directly on the passenger. Choice C is incorrect because the Third Law describes action-reaction pairs between two objects, which is not the key concept here. Choice D is incorrect because gravity pulls downward, not forward.

Question 2: BASIC CALCULATION

A net force of 60 N is applied to a 20 kg shopping cart. Using Newton's Second Law (F = m × a), what is the acceleration of the cart?

A. 1,200 m/s²
B. 3 m/s²
C. 40 m/s²
D. 0.33 m/s²

Show answer (B)

The correct answer is B. Using F = m × a, we rearrange to a = F ÷ m = 60 N ÷ 20 kg = 3 m/s². Choice A (1,200) results from mistakenly multiplying F × m instead of dividing. Choice C (40) comes from subtracting (60 − 20) instead of dividing. Choice D (0.33) results from dividing in the wrong order (m ÷ F = 20 ÷ 60). Always check that you are dividing force by mass when solving for acceleration.

Question 3: INTERMEDIATE

A researcher tests how force affects the acceleration of a 5 kg cart on a low-friction track. The data are shown below. Trial 1: Force = 10 N, Acceleration = 2.0 m/s² Trial 2: Force = 20 N, Acceleration = 4.0 m/s² Trial 3: Force = 30 N, Acceleration = 6.0 m/s² Trial 4: Force = 40 N, Acceleration = 8.0 m/s² Based on the data, what would be the expected acceleration if the applied force is increased to 50 N?

A. 8.0 m/s²
B. 10.0 m/s²
C. 12.5 m/s²
D. 50.0 m/s²

Show answer (B)

The correct answer is B. The data shows a consistent linear relationship: each 10 N increase in force produces a 2.0 m/s² increase in acceleration. This matches F = m × a with m = 5 kg, since a = F ÷ 5. For 50 N: a = 50 ÷ 5 = 10.0 m/s². Choice A simply repeats the Trial 4 value without extending the pattern. Choice C (12.5) comes from dividing 50 by 4 (confusing the trial number for the mass). Choice D (50.0) ignores the mass entirely, treating force and acceleration as equal, which only works if mass is 1 kg.

Question 4: APPLIED

2 pts

A car traveling at 25 m/s on a highway applies its brakes and comes to a complete stop in 5 seconds. The car has a mass of 1,500 kg. Using Newton's Second Law, explain how to calculate the braking force on the car. Include your calculation and state the direction of the force relative to the car's motion.

Show answer

Rubric (2 points): Point 1 — Correct calculation: First find acceleration: a = (v_final − v_initial) ÷ time = (0 − 25) ÷ 5 = −5 m/s². Then find force: F = m × a = 1,500 × (−5) = −7,500 N. The braking force is 7,500 N. Point 2 — Correct direction and reasoning: The braking force acts in the direction opposite to the car's motion (backward). The negative sign indicates deceleration — the car is slowing down. According to Newton's Second Law, a net force in the opposite direction to motion produces a negative acceleration, which reduces the car's velocity until it stops.

Question 5: CRITICAL THINKING

3 pts

A student conducts an experiment to test Newton's Second Law. She uses a cart on a track and applies the same force (10 N) while varying the mass of the cart. Her results are shown below: Trial 1: Mass = 2 kg, Acceleration = 4.8 m/s² Trial 2: Mass = 4 kg, Acceleration = 2.3 m/s² Trial 3: Mass = 6 kg, Acceleration = 1.5 m/s² Trial 4: Mass = 8 kg, Acceleration = 1.1 m/s² According to F = m × a, the predicted accelerations at 10 N should be 5.0, 2.5, 1.67, and 1.25 m/s² for each trial. Analyze the data. (1) Describe the overall pattern shown in the data and whether it supports Newton's Second Law. (2) Identify a likely source of error that could explain why the measured accelerations are slightly lower than predicted. (3) Suggest one improvement to the experimental design that could reduce this error.

Show answer

Rubric (3 points): Point 1 — Pattern and support for Newton's Second Law: The data shows that as mass increases, acceleration decreases. This inverse relationship is consistent with Newton's Second Law (a = F ÷ m), which predicts that for a constant force, doubling the mass should halve the acceleration. The data generally supports the law. Point 2 — Source of error: The measured accelerations are consistently lower than predicted, suggesting that friction on the track is reducing the net force below 10 N. Some of the applied 10 N force goes toward overcoming friction, leaving less force to accelerate the cart. This systematic error affects every trial. Point 3 — Improvement: The student could reduce friction by using an air track (which floats the cart on a cushion of air), or she could measure the friction force separately and subtract it from the applied force to calculate the true net force. Either change would bring the measured accelerations closer to the predicted values.

SUMMARY

Lesson Summary

Summary

Newton's First Law (Inertia) tells us that an object at rest stays at rest and an object in motion stays in motion at constant velocity unless acted upon by an unbalanced net force. Newton's Second Law quantifies this with the equation F = m × a, meaning that acceleration depends on both the net force applied and the object's mass. Newton's Third Law states that every action has an equal and opposite reaction, with the two forces acting on different objects.

On the GED Science test, remember to identify the net force before calculating acceleration. Watch for common distractors based on misconceptions like "objects need a constant force to keep moving" or "heavier objects fall faster." Use free-body diagrams to visualize forces, add or subtract forces to find the net force, and then apply F = m × a. With these tools, you can confidently tackle any motion and force question on the exam.