Lesson · P.1.1

Speed and velocity

The difference between distance and displacement, why velocity is speed with a direction attached, and how to calculate average speed using v = d / t, the formula the HESI A2 physics subtest returns to in nearly every motion question.

ObjectiveP.1.1Read4 minExam weightMotion ≈ 24% of Physics

By the end of this lesson you can

You can explain the difference between distance and displacement for the same trip, including a trip that ends up back where it started.
You can say why velocity is a vector and speed is a scalar, and report a velocity together with its direction.
You can calculate average speed from a total distance and a total time, using v = d / t, including a trip made up of more than one leg.

Key takeaways

Distance is the total path length covered and never runs backward; displacement is the straight-line change from start point to end point and can equal zero even after a long trip.
Speed is a scalar, a number and a unit with no direction attached; velocity is a vector, the same kind of number reported together with a direction.
Average speed is v = d / t, total distance divided by total time; average velocity is total displacement divided by total time instead, and the two numbers can differ a great deal for the same trip.
A trip that finishes exactly where it started always has an average velocity of zero, no matter how far or how fast that trip actually covered.
Gravity adds 9.8 m/s of downward speed to a freely falling object for every second it falls (g = 9.8 m/s²), a constant the next lesson builds acceleration on.

Check yourself

0 / 5

1A courier drives 12 km from the office to a client site, then drives the same 12 km back to the office along the same road. Which statement correctly compares the trip's distance and displacement?
2A cyclist rides a total of 30 kilometres in 2 hours without stopping along the way. What is the cyclist's average speed for the whole ride?
3A wrench slips out of a mechanic's hand and falls freely from rest for 5 seconds before hitting the floor. Taking g = 9.8 m/s², what speed has the wrench reached at the moment it lands?
4Which option correctly labels each quantity as a vector or a scalar?
5Two delivery vans both travel at 80 km/h along the same motorway, but one heads north and the other heads south. What can be concluded about their velocities?

Practise more →

Distance and displacement

Distance is the total length of the path something actually covers. It only ever adds up, metre by metre, no matter how the path curves or doubles back on itself. Displacement measures something else: the straight-line change from where an object started to where it ended up, reported together with a direction. The two agree only when a trip runs in one straight line without doubling back.

Step counter versus displacement. A nurse's fitness tracker can log several kilometres of walking across one busy shift, all of it real distance. If that nurse starts and ends the shift at the same nurses' station, the shift's net displacement is still zero, however high the step count reads.

Why velocity needs a direction

A quantity that stands complete as a number and a unit is a scalar. Distance is a scalar, and so is speed. A quantity that only becomes complete once a direction is attached is a vector. Displacement is a vector, and so is velocity, which is speed reported together with a direction of travel.

This is not a technicality the exam drops for convenience. Two ambulances can both be travelling at exactly 60 km/h and still have completely different velocities if one heads north out of the depot while the other heads south. Their speedometers would read identically. Their velocities would not.

Calculating average speed

Average speed only ever asks for two numbers, the total distance covered and the total time it took, one divided by the other.

Quantity	Formula	Vector or scalar
Distance	total path length covered	Scalar
Displacement	straight-line change in position	Vector
Average speed	v = d / t	Scalar
Average velocity	v = displacement / t	Vector

Quantity

Formula

Vector or scalar

Distance

total path length covered

Scalar

Displacement

straight-line change in position

Vector

Average speed

v = d / t

Scalar

Average velocity

v = displacement / t

Vector

Any consistent pair of units works, metres and seconds or kilometres and hours. The one habit worth automating before exam day is checking that the distance and the time you are dividing belong to the same stretch of the trip, since pairing distance from one leg of a journey with time from a different leg is the fastest way to turn an easy mark into a wrong one.

Speed tells you how fast something is moving; velocity tells you how fast and in which direction.

Once distance versus displacement and speed versus velocity both feel automatic, the next lesson in this unit builds straight on top of them: acceleration, the rate at which velocity itself changes over time. The 9.8 m/s² you just met does not disappear. It becomes the constant behind every falling or thrown object you work through next.