Speed is distance ÷ time, velocity is speed with a direction, and acceleration is the change in velocity ÷ time. Keep the units consistent and the answer follows.
This lesson starts the force and motion topic. When you finish, continue with reading motion graphs.
What are the three formulas?
| Quantity | Formula | Unit |
|---|---|---|
| Speed | distance ÷ time | m/s |
| Velocity | displacement ÷ time, with direction | m/s |
| Acceleration | (final velocity − initial velocity) ÷ time | m/s² |
Speed has a size only. Velocity has a size and a direction, which is why a runner going round a full lap can have a speed but an average velocity of zero at the finish line.
Worked example: a fictional cyclist
An invented cyclist travels 18 km in 45 minutes at a steady pace. The question asks for speed in m/s.
Step 1: convert the units. 18 km = 18 000 m, and 45 minutes = 45 × 60 = 2 700 s.
Step 2: substitute. Speed = 18 000 ÷ 2 700.
Step 3: calculate. 18 000 ÷ 2 700 = 6.67 m/s to 3 significant figures.
Step 4: check for sense. 6.67 m/s is about 24 km/h, since 6.67 × 3.6 = 24. That is a reasonable cycling speed.
Now an acceleration question using the same cyclist. She speeds up from 2 m/s to 8 m/s in 4 s going east. Acceleration = (8 − 2) ÷ 4 = 6 ÷ 4 = 1.5 m/s² east.
The mistake that costs marks
The common slip is to substitute mixed units: 18 ÷ 45 = 0.4, then write “0.4 m/s”. The number is in km per minute, so the unit written is wrong, and the answer is nowhere near 6.67 m/s.
The fix is to convert both the distance and the time before you substitute. Write the converted values on their own line so you can see them.
Check yourself
An invented train slows from 25 m/s to 10 m/s in 6 s while travelling north. Calculate the acceleration and say what the sign means.
Answer
Acceleration = (10 − 25) ÷ 6 = −15 ÷ 6 = −2.5 m/s².
The negative sign means the velocity is decreasing in the direction of travel, so the train is slowing down. The size of the slowing is 2.5 m/s every second.
What to study next
Next, see the same quantities as shapes in reading motion graphs, or go back to the force and motion overview. The motion-graph explorer draws the graph for any speed you choose.
To keep track of unit errors, use the mistake log and paper-error review. If you want a teacher checking your working as you go, see online one-to-one Science tuition.