1.1.1 · PY-11-01
Classify distance, displacement, time, speed, velocity and acceleration as either scalar or vector quantities
Theory & examples
Practice
Quiz
Worksheet
What are scalar and vector quantities?
Every measurement in physics is classified by whether direction matters:
Scalar
Magnitude only — a number and a unit. No direction needed.
Vector
Magnitude AND direction — incomplete without both.
Exam tip: Always state direction for vector answers — e.g. “15 m s⁻¹ east”. Missing direction = lost marks.
Worked examples
1
Classifying a list of quantities
Easy
Classify each as scalar or vector: (a) 25 m s⁻¹ (b) 9.8 m s⁻² downward (c) 3.5 km (d) 12 s (e) 60 km h⁻¹ north
Getting started: Ask — does each quantity include a direction word like “north” or “downward”? Yes → vector. No → scalar.
1
Strategy
Direction word present → vector. No direction → scalar.
2
Answers
(a) scalar (speed) (b) vector (acceleration) (c) scalar (distance) (d) scalar (time) (e) vector (velocity)
2
Distance vs displacement
Easy
A student walks 300 m east to a bus stop, then 100 m west. (a) Total distance? (b) Displacement?
Getting started: Distance = total path — add all distances. For displacement, let east = positive and apply + or − to each leg.
1
Distance
300 + 100 = 400 m
2
Displacement
+300 − 100 = 200 m east
3
Speed vs velocity — full lap
Easy
A car completes one full lap of a 2 km circular track in 80 s. (a) Average speed? (b) Average velocity?
Getting started: Use speed = distance ÷ time. For velocity, think — where does the car start and finish after one full lap?
1
Average speed
2000 ÷ 80 = 25 m s⁻¹
2
Average velocity
Returns to start → displacement = 0 → 0 m s⁻¹
4
Identifying vectors in real-world context
Medium
Wind blows at 40 km h⁻¹ from the south-west. A speedometer reads 80 km h⁻¹. Which is a vector and which is a scalar?
Getting started: Does either measurement tell you which direction something is moving? A speedometer only shows how fast — not which way.
1
Wind
“From south-west” gives direction → vector (velocity)
2
Speedometer
No direction → scalar (speed)
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