A scalar has magnitude only: mass, time, temperature. A vector also has direction: displacement, velocity, force.
Vector A quantity with both magnitude and direction.
Step 1: Something to Notice
Watch first. The explanation comes later.
Walk 3 km north and then 4 km south. You have walked 7 km, and you are 1 km from where you started.
Which of those two numbers is the answer, and to what question?
Step 2: Find Out
Isolate a motion in the negative direction and check whether the negative sign implies slowing.
Step 1 — Predict
A car has a constant velocity of −12 m/s. What is it doing?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
Distance and displacement differ
Distance is the path length; displacement is the straight-line change in position, with direction.
The sign is a direction
Once an axis is chosen, a minus means the other way. It says nothing about magnitude changing.
SI units, and checking with them
Meters, kilograms, seconds. An equation whose units do not match is wrong before any number is put in.
And measurements carry uncertainty
Every measured value has a precision, and a calculated result cannot be more certain than its inputs.
Some quantities need a direction
Speed is a scalar and velocity is a vector. Distance is a scalar and displacement is a vector. A round trip has a large distance and zero displacement, which is why the distinction is not pedantry.
Units check the physics
An equation whose two sides have different units is wrong, whatever the algebra. Dimensional checking catches errors before any number is substituted and costs almost nothing.
Step 4: A Common Mistake
Lots of people think
“A negative velocity means slowing down.”
Step 5: Why SI Units Are Defined by Constants Now
The same idea somewhere new.
Every SI base unit is now fixed by assigning an exact value to a constant of nature — the second by a caesium frequency, the meter by the speed of light, the kilogram by the Planck constant since 2019. No physical artefact is involved any more, which matters because the old kilogram prototype in Paris was measurably drifting against its copies and nobody could say which had changed.
Step 6: Think It Through
Practice makes it stick.
There and Back
Problem 1 of 2
You walk 3 km north then 4 km south. What is your displacement?
A Negative Velocity
Problem 2 of 2
A car has a steady velocity of −12 m/s. Is it slowing down?
Magnitude and Direction
1 of 5
Which of these are vectors?
2 of 5
What does a negative sign on a velocity mean?
3 of 5
Is v = at² dimensionally correct?
4 of 5
You walk 5 km east and 5 km west. What is your displacement?
5 of 5
How is the kilogram defined now?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Does a negative velocity mean an object is slowing down?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain the difference between distance and displacement, and why a negative velocity does not mean slowing down.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- Scalars have magnitude only; vectors have magnitude and direction.
- Distance is path length; displacement is the straight-line change with direction.
- The sign of a vector is a direction and says nothing about magnitude changing.
- Units that do not match make an equation wrong before any number is used.