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Introduction to Motion

Describing Movement

Physics often starts with motion because everything in the universe is moving. To understand why things move, we first need a clear way to describe how they move. This means talking about where something is, how fast it's going, and how its movement changes.

Let's begin with the simplest question: Where is it? An object's position is just its location. But what happens when that position changes? That's motion, and it brings us to two very important ideas: distance and displacement.

Distance and Displacement

These two words sound similar, but in physics, they mean different things. Distance is the total length of the path you travel. If you walk two miles to a friend's house and two miles back, you've traveled a distance of four miles. It's a simple measurement of how much ground you covered.

Displacement is different. It's the change in your position from your starting point to your ending point, measured in a straight line. In that walk to your friend's house and back, your starting point was your home and your ending point was also your home. So, even though you walked four miles, your displacement is zero.

Distance just tells you "how much," while displacement tells you "how much and in what direction." Because displacement includes direction, it's known as a vector quantity. Distance, which has no direction, is a scalar quantity. This distinction becomes very important when we talk about speed and velocity.

Displacement

noun

The change in an object's position, measured as a straight line from the start point to the end point.

Speed and Velocity

Just like distance and displacement, speed and velocity are a pair of concepts that are related but distinct. Speed is how fast an object is moving. If a car's speedometer reads 60 miles per hour, that's its speed. It's a scalar quantity, meaning it only tells you the rate of motion.

Speed is calculated by dividing the distance traveled by the time it took.

Velocity, on the other hand, is an object's speed in a specific direction. So, saying a car is moving at 60 miles per hour east describes its velocity. Because it has both a magnitude (60 mph) and a direction (east), velocity is a vector quantity.

A car driving on a circular racetrack at a constant 100 mph has a constant speed. But its velocity is constantly changing because its direction is always turning. Anytime an object's direction changes, its velocity changes, even if its speed does not.

Average Speed=DistanceTimevavg=ΔxΔt\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \\ \\ \vec{v}_{\text{avg}} = \frac{\Delta \vec{x}}{\Delta t}

Acceleration

What happens when velocity changes? That's acceleration. In everyday language, we think of acceleration as just speeding up. In physics, it's much broader.

Acceleration

noun

The rate at which an object's velocity changes over time.

Because velocity includes both speed and direction, you are accelerating if you:

  1. Speed up
  2. Slow down (this is often called deceleration)
  3. Change your direction of travel

That car on the racetrack? It's constantly accelerating because its direction is constantly changing. A ball thrown straight up into the air is also accelerating. Its speed decreases on the way up and increases on the way down, all while gravity pulls it downward.

aavg=ΔvΔt=vfvitfti\vec{a}_{\text{avg}} = \frac{\Delta \vec{v}}{\Delta t} = \frac{\vec{v}_{f} - \vec{v}_{i}}{t_{f} - t_{i}}

Understanding these three concepts, displacement, velocity, and acceleration, gives us the basic language we need to describe any kind of motion accurately.

Quiz Questions 1/5

A runner completes exactly one lap around a 400-meter circular track, ending at the exact same point they started. What are their total distance traveled and their total displacement?

Quiz Questions 2/5

In physics, which of the following statements best describes the difference between speed and velocity?