Motion: How Things Move

Speed, velocity, and acceleration explained so they finally make sense.

Start with a question

You’re in a car going down the highway. The speedometer says 100 km/h. Simple, right?

Now answer this: are you moving?

• Compared to the road? Yes, 100 km/h.
• Compared to the person in the passenger seat? No. Not at all. You’re sitting still next to them.

That’s the first secret of motion: motion is always relative to something else. There’s no such thing as “just moving.” You’re always moving compared to something.

Keep that in your pocket. It explains a lot.

Speed vs. velocity (the real difference)

School tells you these are different and then never explains why. Here’s why.

Speed

How fast. Just a number.

“I’m going 60 km/h.”

Velocity

How fast and which way. A number plus a direction.

“I’m going 60 km/h north.”

Why direction matters

Imagine two cars, both doing 60 km/h, heading straight at each other. Same speed. But they’re about to crash — because their velocities are opposite.

Now imagine two cars doing 60 km/h side by side on the highway. Same speed, same velocity. They’ll never crash.

Direction isn’t a fussy detail. Direction is the difference between a peaceful drive and a head-on collision. That’s why engineers always track it.

Anything with a direction baked in is called a vector. Anything that’s just a number is a scalar. Velocity = vector. Speed = scalar. You’ll see those words a lot.

Acceleration: the most misunderstood word in physics

In everyday English, “accelerate” means “speed up.” In physics, it means something bigger:

Acceleration = any change in velocity.

That includes:

• Speeding up (pressing the gas)
• Slowing down (pressing the brake)
• Turning (changing direction even at the same speed)

Yes, turning a corner at constant speed is acceleration. That feels weird, but it’s true — because your velocity (which includes direction) is changing.

The feeling test

Here’s a trick: if your body feels pushed into the seat, you’re accelerating.

• Floor it from a stoplight → pushed back → acceleration.
• Slam the brakes → pushed forward → acceleration (just negative).
• Sharp left turn → pushed right → acceleration.
• Cruising on the highway → no push → no acceleration, even at 120 km/h.

If nothing is pushing you, your velocity isn’t changing. Simple as that.

The three equations that run everything

For an object speeding up at a steady rate, three equations cover almost every problem. Don’t memorize them yet — just read what they mean.

1. Final velocity

   $v = v_0 + at$

   “My new speed = my old speed + (how hard I’m accelerating × how long I’ve been doing it).”

   Floor a car at 3 m/s² for 5 seconds and you gained 15 m/s. Obvious when you read it slowly.

2. Distance traveled

   $d = v_0 t + \tfrac{1}{2} a t^2$

   “How far I went = how far I’d have gone at my old speed + the extra distance from speeding up.”

   The $\tfrac{1}{2} a t^2$ part is the bonus distance you get because you’re getting faster as you go.

3. Velocity from distance

   $v^2 = v_0^2 + 2ad$

   “If I don’t care about time, just distance, here’s how fast I’ll be going.”

   This one is gold for stopping-distance problems.

A worked example you can actually feel

Problem: You’re stopped at a red light. It turns green. You accelerate at 2 m/s². How fast are you going after 4 seconds, and how far did you travel?

Step 1 — picture it. A car going from 0 to something. Pretty boring scene. Good.

Step 2 — list what you know.

• Starting speed $v_0 = 0$ m/s (you were stopped)
• Acceleration $a = 2$ m/s²
• Time $t = 4$ s

Step 3 — pick the recipe.

We want final speed → use equation 1.

$v = 0 + (2)(4) = 8 \text{ m/s}$

That’s about 29 km/h. Reasonable for 4 seconds of gentle acceleration.

We want distance → use equation 2.

$d = (0)(4) + \tfrac{1}{2}(2)(4)^2 = 16 \text{ m}$

You covered 16 meters. About 4 car-lengths. Also reasonable.

Notice we never “did physics.” We pictured a car, listed what we knew, and picked the recipe that used those ingredients. That’s the whole skill.

The biggest misconception

“If something is moving, a force must be pushing it.”

False. This is what Aristotle thought for 2,000 years and what your brain still secretly believes. The truth (Newton figured it out): things in motion stay in motion until something stops them. A hockey puck on perfect ice would slide forever.

We’ll unpack that on the next page, because it’s the gateway to understanding every force in the universe.

Next: Forces and Newton's Laws

Why things start moving, stop moving, and push back when you push them.