Every quantity in physics is either a scalar or a vector. Getting this right matters for forces, motion and momentum. Answer each question on paper first, then tap to check. Questions marked (H) are Higher tier. ← Forces topic
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A SCALAR quantity has magnitude (size) only.
A VECTOR quantity has magnitude AND direction.
A vector can be shown by an arrow: the length shows the magnitude and the arrow shows the direction.
Because vectors have a direction, they can be NEGATIVE (e.g. −12 m/s means 12 m/s in the opposite direction).
| Scalar | Matching vector |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Weight (a force) |
| Time, energy, temperature, power | Force, acceleration, momentum |
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Forces are vectors. CONTACT forces act when objects touch: friction, air resistance, tension, normal contact force, upthrust.
NON-CONTACT forces act at a distance: gravitational, electrostatic, magnetic.
Foundation and Higher
Q1 (2 marks) Sort these into scalars and vectors: mass, velocity, distance, force, time, acceleration, energy, displacement, speed, weight, momentum, temperature.
Show solution
Scalars: mass, distance, time, energy, speed, temperature (1)
Vectors: velocity, force, acceleration, displacement, weight, momentum (1)
Q2 (2 marks) What is the difference between speed and velocity?
Show solution
Speed is a scalar – it only has a size, e.g. 20 m/s (1). Velocity is a vector – it is speed in a given direction, e.g. 20 m/s north (1).
Q3 (2 marks) Explain why weight is a vector but mass is a scalar.
Show solution
Weight is a force, so it has a size and a direction – towards the centre of the Earth (1). Mass is the amount of matter in an object – it has a size but no direction (1).
Q4 (2 marks) Jo walks 30 m east, then turns round and walks 40 m west. Calculate (a) the distance she walks and (b) her displacement.
Show solution
(a) Distance = 30 + 40 = 70 m (1)
(b) Displacement = 40 − 30 = 10 m west (1) – you need the direction for the mark.
Q5 (2 marks) An athlete runs exactly one lap of a 400 m track, finishing where she started. What is (a) the distance and (b) the displacement?
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(a) 400 m (1)
(b) 0 m (1) – she finishes at her starting point, so the straight-line distance from start to finish is zero.
Q6 (2 marks) A car drives round a roundabout at a steady 10 m/s. Is its speed constant? Is its velocity constant? Explain.
Show solution
The speed is constant (10 m/s) (1). The velocity is changing, because the car’s direction keeps changing and velocity includes direction (1).
Q7 (1 mark) On a force diagram, the scale is 1 cm = 10 N. An arrow is 4.5 cm long and points to the left. What force does it represent?
Show solution
4.5 × 10 = 45 N to the left (1)
Q8 (2 marks) Classify each force as contact or non-contact: friction, gravity, tension, magnetic force, air resistance, electrostatic force, normal contact force, upthrust.
Show solution
Contact: friction, tension, air resistance, normal contact force, upthrust (1)
Non-contact: gravity, magnetic force, electrostatic force (1)
Q9 (2 marks) Two cars both travel at 25 m/s on the same road, one heading north and one heading south. Do they have the same speed? The same velocity? Explain.
Show solution
Same speed (25 m/s) (1), but different velocities, because they are moving in opposite directions – 25 m/s north and 25 m/s south (1).
Q10 (2 marks) Using a scale of 1 cm = 5 m/s, draw arrows to represent (a) a velocity of 20 m/s east and (b) a velocity of 15 m/s north.
Show solution
(a) An arrow 4.0 cm long pointing right (east) (1)
(b) An arrow 3.0 cm long pointing up the page (north) (1)
Both arrows need an arrowhead and a label.
Q11 (2 marks) Which two of these quantities can have a negative value: speed, velocity, distance, displacement? Explain why.
Show solution
Velocity and displacement (1). They are vectors, so the minus sign shows the direction – opposite to the direction chosen as positive. Speed and distance are scalars and can’t be negative (1).
Higher tier
Q12 (3 marks – H) A walker goes 3.0 km north, then 4.0 km east. Calculate (a) the total distance and (b) the size of the displacement. (c) Describe the direction of the displacement.
Hint: draw the two journeys head-to-tail. The displacement is the straight line from start to finish – use a scale drawing or Pythagoras.
Show solution
(a) Distance = 3.0 + 4.0 = 7.0 km (1)
(b) Displacement = √(3.0² + 4.0²) = √25 = 5.0 km (1)
(c) Between north and east – about 53° east of north (a bearing of 053°) (1)
Q13 (2 marks – H) A ball is thrown straight up at 12 m/s. A moment later it falls back past the same point at 12 m/s. Compare its speed and velocity at these two moments.
Show solution
The speed is the same both times (12 m/s) (1). The velocity is different: +12 m/s (upwards) on the way up and −12 m/s (downwards) on the way down – the sign shows the direction (1).
Q14 (3 marks – H) A satellite orbits the Earth at a constant speed. Explain why it is accelerating.
Show solution
Its direction is constantly changing (1), so its velocity is changing, because velocity is a vector (1). Acceleration is the rate of change of velocity, so it is accelerating – towards the centre of the orbit, due to gravity (1).
✅ Add up your marks out of 29 (or out of 21 for Q1–Q11 if you’re doing Foundation).
⚠️ Where students lose marks
- Leaving out the direction when asked for a displacement or velocity – “10 m” scores 0; “10 m west” scores the mark.
- Treating displacement as distance. Displacement is the straight line from start to finish, not the length of the route.
- Calling weight a scalar or mixing up mass and weight. Weight is a force, in newtons, with a direction.
- Saying gravity is a contact force. Gravity, magnetic and electrostatic forces act at a distance.
- Thinking constant speed means constant velocity. If the direction changes, the velocity changes.
Next: Resultant forces →
