What is the difference between speed and velocity?

Speed only tells you how fast something moves. Velocity tells you how fast AND in which direction. So '30 m/s' is a speed, but '30 m/s north' is a velocity. Velocity is what physicists call a vector because it includes direction.

Why do we use metres per second in physics?

Metres per second (m/s) are the standard scientific units because metres and seconds are SI base units, which makes calculations consistent. In everyday life we often use kilometres per hour or miles per hour instead, but the maths works the same way.

Speed, Distance and Time | Physics

What does it mean to be "fast"?

We use the word fast all the time — a fast car, a fast runner, a fast train. But what does "fast" actually mean in physics? It means covering a lot of distance in a small amount of time. A cheetah is fast because it can cover 100 metres in just a few seconds; a snail is slow because the same distance would take it hours.

This relationship between how far you go and how long it takes is captured by one of the most useful ideas in physics: speed. Once you understand the link between speed, distance and time, you can predict journeys, read graphs of motion, and solve a huge range of problems. (For a gentler first look at the idea, you can also visit fast and slow speed.)

The speed formula

Speed is defined as the distance travelled in each unit of time. The formula is:

Speed = distance ÷ time

Or using symbols: v = d ÷ t, where v is speed, d is distance and t is time.

In science we usually measure:

distance in metres (m),
time in seconds (s),
so speed comes out in metres per second (m/s).

A speed of 5 m/s means the object covers 5 metres every single second. Everyday speeds are often given in kilometres per hour (km/h) or miles per hour (mph) instead, but the idea is identical.

Rearranging the formula

The real power comes from rearranging the formula to find whichever quantity you don't know. There are three versions, all from the same equation:

To find speed: speed = distance ÷ time
To find distance: distance = speed × time
To find time: time = distance ÷ speed

A handy way to remember this is the formula triangle. Write d on top, with v and t underneath:

      d
    -----
    v | t

Cover the quantity you want, and the triangle shows you the calculation. Cover d and you see v × t. Cover v and you see d ÷ t. Cover t and you see d ÷ v.

Worked examples

Example 1 — finding speed. A sprinter runs 100 metres in 12.5 seconds. What is their average speed?

Speed = distance ÷ time = 100 ÷ 12.5 = 8 m/s

Example 2 — finding distance. A train travels at 55 m/s for 200 seconds. How far does it go?

Distance = speed × time = 55 × 200 = 11 000 m (that's 11 km)

Example 3 — finding time. A cyclist needs to cover 1500 m and rides at a steady 6 m/s. How long will it take?

Time = distance ÷ speed = 1500 ÷ 6 = 250 s (which is 4 minutes 10 seconds)

Notice that you must keep your units consistent. If distance is in metres and time in seconds, the speed is in m/s. Mixing kilometres and seconds, for instance, would give a wrong answer.

Average speed vs instantaneous speed

Real journeys are rarely at one steady speed — you speed up, slow down, and stop at traffic lights. So we use two ideas:

Average speed is the total distance divided by the total time for the whole journey. It smooths over all the speeding up and slowing down.
Instantaneous speed is the speed at one particular instant — what a car's speedometer shows right now.

Worked example. A family drives 150 km in 3 hours, including a lunch stop. Their average speed is:

Speed = 150 ÷ 3 = 50 km/h

Even though at some moments they were doing 100 km/h on the motorway and at other moments 0 km/h while parked, the average for the trip was 50 km/h.

Distance-time graphs

A distance-time graph is a brilliant way to picture a journey. Time goes along the bottom (x-axis) and distance goes up the side (y-axis). The shape of the line tells the whole story:

A flat (horizontal) line → the distance is not changing → the object is stationary.
A straight sloping line → the object moves at a constant speed.
A steeper line → a faster speed (more distance covered in the same time).
A curved line getting steeper → the object is accelerating (speeding up).

The really useful trick: the gradient (steepness) of a distance-time graph equals the speed. You calculate it just like the formula — the change in distance divided by the change in time. A line that rises 40 m over 8 s has a gradient of 40 ÷ 8 = 5 m/s, which is the speed.

Speed, velocity and direction

One last subtlety. Speed tells you only how fast something moves. Velocity tells you how fast and in which direction. So "20 m/s" is a speed, but "20 m/s east" is a velocity. This matters when direction changes — a car going round a roundabout at a steady 20 m/s has constant speed but constantly changing velocity, because its direction keeps changing. Changing velocity links directly to forces and acceleration, which you can explore in Newton's laws of motion.

Try it yourself! 🧪

Measure your own walking and running speed.

You need a tape measure or a known distance (a hallway, garden path or playground), a stopwatch (a phone works), and a friend.

Measure out a straight distance — say 10 metres — and mark the start and finish.
Have your friend time you with the stopwatch as you walk from start to finish. Record the time in seconds.
Calculate your walking speed: speed = distance ÷ time. For example, if 10 m took 8 s, your speed is 10 ÷ 8 = 1.25 m/s.
Now run the same 10 metres and time it again. Calculate your running speed. It should be much higher!
Bonus: time yourself over a longer distance (say 50 m) and find your average speed. Compare it to your 10 m sprint — your average over the longer distance is usually a little lower, because you cannot keep top speed the whole way.

You have now used speed = distance ÷ time with real measurements, exactly the way scientists and sports coaches do.

Speed, Distance and Time

Key takeaways