1D-Motion Introduction

One-dimensional motion describes how objects move along a straight line. Whether it's a car speeding up on a highway or a ball dropping from your hand, understanding these basics helps explain the physical world around you.

This guide covers the essential concepts of 1D-motion, from basic measurements to equations that predict movement. We'll explore both the simple ideas (like distance) and more complex concepts (like acceleration).

Remember: One-dimensional motion only deals with movement forward and backward along a single line—like moving along a number line in math class!

Scalar Quantities

A scalar is simply a measurement that only tells you "how much" without specifying direction. Think of it as just a plain number with units.

When you say "I rode my bike 12 mph," you're using a scalar quantity—you're stating speed without mentioning which way you're going. Other examples include temperature (80°F), mass (5 kg), or time (3 hours).

Scalars are the simpler measurement type in physics since they don't require directional information. You'll use them frequently when precise direction isn't important to your calculation.

Quick Tip: Whenever a measurement doesn't need an arrow to represent it fully, it's probably a scalar!

Vector Quantities

A vector provides both magnitude (size) and direction, often shown with an arrow in diagrams. The arrow's length represents the magnitude, while its orientation shows direction.

When you say "I rode my bike 12 mph north," you're using a vector quantity—you're specifying both how fast and which way. This complete information makes vectors essential for accurately describing motion.

In your physics homework, you'll recognize vectors by words like "north," "upward," or "to the right" attached to measurements.

Pro Tip: When a problem includes direction words like "northwest" or "downward," you're definitely dealing with vectors!

Position

Position describes exactly where something is located in space. It's a vector quantity because it needs both a distance and a direction from a reference point (origin).

When we say "The president is 20 meters above the ground on stage," we're giving position information. The reference point is the ground, the distance is 20 meters, and the direction is "above."

On a number line or coordinate system, positions are typically marked with letters (like points A, B, C) and measured in meters. The reference point (origin) is usually labeled as zero.

Physics Connection: Position is the foundation for all motion calculations—you need to know where something starts before you can figure out how it moves!

Displacement

Displacement measures how far an object has moved from its starting position, regardless of the path taken. It's a straight-line measurement from start to finish.

Imagine walking in a square pattern—5m east, 3m north, 5m west, and 3m south. Even though you walked 16 meters total, your displacement would be zero because you ended up back at your starting point!

Displacement is a vector because it includes both the direct distance between start and finish points AND the direction. It's written with both a number and a direction (like "4 meters east").

Important Distinction: Displacement tells you the "as-the-crow-flies" distance between two positions, not how much ground you covered getting there.

Distance

Distance measures the total length of the path traveled, regardless of direction or ending position. It only cares about how far you went, not where you ended up.

If you bike 9 miles east and then 9 miles west, your total distance is 18 miles, even though you ended up back where you started. This makes distance a scalar quantity—just a number with units.

Unlike displacement, distance can never be negative or zero (unless you didn't move at all). It always represents the actual ground covered during movement.

Real-World Connection: Your car's odometer measures distance, not displacement—it counts all the miles you drive regardless of whether you end up back in your driveway!

Velocity

Velocity measures how quickly an object's position changes and in what direction. It's calculated by dividing displacement by time $V = d/t$.

Unlike speed, velocity is a vector quantity because it includes direction. Saying a car moves at "60 mph eastbound" gives its velocity, while just "60 mph" only indicates speed.

Velocity can be positive (moving in the positive direction), negative (moving in the negative direction), or zero (not moving). When velocity changes—either speeding up, slowing down, or changing direction—acceleration is happening.

Visualization Tip: On a position-time graph, velocity is represented by the slope of the line. A steeper slope means higher velocity!

Speed

Speed tells you how fast something is moving without specifying direction. It's the rate at which an object covers distance over time.

Speed is calculated by dividing the total distance traveled by the time taken. For example, if you drive 120 miles in 2 hours, your average speed is 60 miles per hour.

As a scalar quantity, speed only gives magnitude—the "how fast" part of motion. It's always positive (or zero) and doesn't tell you which way the object is moving.

Everyday Example: Your car's speedometer shows speed (how fast you're going) but doesn't indicate direction—that's why it's never negative!

Acceleration

Acceleration measures how quickly velocity changes over time. It occurs whenever an object speeds up, slows down, or changes direction.

The formula for acceleration is simple: acceleration = change in velocity ÷ change in time. If a car increases its velocity from 0 to 60 mph in 6 seconds, its acceleration is 10 mph per second.

Acceleration can be positive (speeding up in the positive direction or slowing down in the negative direction) or negative (slowing down in the positive direction or speeding up in the negative direction).

Common Misconception: Acceleration doesn't always mean speeding up! When you hit the brakes in a car, you're experiencing negative acceleration (deceleration).

Motion Graphs

Motion graphs visually represent how position, velocity, and acceleration change over time, making complex motion easier to understand.

In a position-time graph, the slope represents velocity. A steeper line means faster movement, while a horizontal line indicates the object isn't moving.

In a velocity-time graph, the slope shows acceleration, while the area under the curve gives displacement. Similarly, in an acceleration-time graph, the area under the curve represents the change in velocity.

Graph Insight: The relationship between these graphs is powerful—what appears as the slope in one graph becomes the value in the next graph. This connection helps solve complex motion problems!