Are we there yet?
Picture a long car journey. Someone in the back seat asks, "How fast are we going?" You look at the speedometer and it says 50. A minute later it's 70. Then you're stuck behind a tractor at 20.
So how fast were you going? That's the question for today. We'll get to grips with three words that sound alike but mean different things: speed, velocity and acceleration. And at the end you'll roll a ball down a slope on your kitchen table and watch them happen.
In Level 1 we looked at units and measuring. Today we put that to work.
Speed: how much ground you cover
Speed tells you how far you travel in a certain amount of time. That's it.
Here's the recipe:
average speed = distance ÷ time
Physicists often write it in shorthand as v = d ÷ t. Let's go through each symbol:
- v is speed (it comes from "velocity", and we'll see why in a moment)
- d is the distance travelled, say in miles, kilometres or metres
- t is the time taken, in hours or seconds
Let's try it. Say you drive 120 miles and it takes 2 hours. What's your average speed?
120 ÷ 2 = 60 miles per hour.
Now, did you go at exactly 60 the whole way? Almost certainly not. You sped up on the motorway, where the limit for cars in the UK is 70 mph. You slowed down in towns and sat in traffic. The average evens all of that out into one number.
The speedometer is different. It shows how fast you're going right now, at this instant. Physicists call that instantaneous speed. Both are useful. They just answer different questions.
One more thing about units. Speed is always a distance unit "per" a time unit. Miles per hour, kilometres per hour, and the scientist's favourite, metres per second (m/s). That's the official unit in the international SI system you met in Level 1.
Velocity: speed with a direction
So if speed is how fast, what's velocity?
Velocity is speed plus direction. "60 mph" is a speed. "60 mph heading north" is a velocity.
Does that difference really matter? Here's a fun case where it does.
You drive 10 miles to the shops and 10 miles back home. The whole trip takes an hour. Your average speed is 20 miles ÷ 1 hour = 20 mph. Fair enough.
But where did you end up? Right where you started. Overall, you didn't get anywhere. So your average velocity for the round trip is zero. Speed counts every mile you drove. Velocity only cares about how far you ended up from your start point, and in which direction.
Think of speed as the number on the dial, and velocity as the dial plus a compass.
Acceleration: how quickly velocity changes
Now for the exciting one. You're waiting at traffic lights. They turn green, you press the pedal, and you feel yourself pushed back into your seat. That's acceleration.
Acceleration measures how quickly your velocity changes. Here's the recipe:
acceleration = change in velocity ÷ time taken
Or in shorthand, a = (v_end − v_start) ÷ t, where:
- a is acceleration
- v_end is the velocity at the end
- v_start is the velocity at the start
- t is the time the change took
Let's try it. A car pulls away from the lights at 0 m/s and reaches 20 m/s after 10 seconds. The change is 20 − 0 = 20 m/s. Divide by 10 seconds and you get 2 metres per second, every second.
That "per second, every second" is why the unit is written m/s² (metres per second squared). It just means the speed goes up by 2 m/s each second that passes.
What about braking? Your velocity is getting smaller, so the acceleration is negative. In everyday speech we call that deceleration.
And here's the sneaky one. Suppose you go round a roundabout at a steady 20 mph. Are you accelerating? Your speed isn't changing... but your direction is. And because velocity includes direction, your velocity is changing. So yes, turning at a steady speed counts as acceleration too. That's why you feel yourself leaning to one side.
Kitchen-table experiment: the rolling ball
Around 400 years ago, Galileo wanted to study falling objects, but they fell too fast to time. His clever trick was to roll balls down a gentle slope, which slows everything down. Let's do the same.
You'll need a long, flat tray or board, a few books, a marble or small ball, a ruler, a pencil or some tape, and the stopwatch on your phone.
- Prop one end of the board on a couple of books to make a gentle slope.
- Measure the full length of the slope. Put a mark at the bottom, and another mark a quarter of the way down from the top.
- Let the ball go from the top. Don't push it! Time how long it takes to reach the bottom. Do this three times and average your times.
- Now time how long it takes just to reach the quarter mark. Again, three tries, then average.
What do you notice? You'll probably find the ball takes about half the total time to cover just the first quarter of the slope. Then it covers the other three quarters in the remaining half of the time.
Why? Because it's speeding up the whole way. It starts at zero and gains speed steadily as it rolls. So it's slow at the top and fast at the bottom. That steady gain in speed is acceleration you can see with your own eyes. Galileo found exactly this pattern.
For a bonus, work out the ball's average speed for the whole slope: length ÷ time. Then add another book and try again. A steeper slope means more acceleration.
Key takeaways
- Average speed = distance ÷ time (v = d ÷ t). A speedometer shows your instantaneous speed instead.
- Velocity is speed with a direction. A round trip back home has an average velocity of zero.
- Acceleration is how quickly velocity changes: change in velocity ÷ time, measured in m/s².
- Speeding up, slowing down and changing direction all count as acceleration.
- A ball rolling down a slope speeds up steadily, so it covers more ground in each second than in the one before.