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AS · Practice questions · Scalars and vectors

Direction matters.

Six original Cambridge-style questions on classifying quantities, resultants, resolving on a slope, and finding a change in velocity by vector subtraction.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Triangle first, then trig.

01
Analysis
[2 marks]

State the difference between a scalar and a vector quantity, and classify each of these: distance, velocity, mass, force.

  • A scalar has magnitude only; a vector has magnitude and direction. ✓
  • Scalars: distance, mass. Vectors: velocity, force. ✓
02
Analysis
[3 marks]

Two forces, 6.0 N due east and 8.0 N due north, act on a point object. Find the magnitude and direction of the resultant force.

  • Magnitude: R = √(6.0² + 8.0²) = √100 = 10 N. ✓
  • Direction: tanθ = 8.0 / 6.0, so θ = 53° north of east. ✓
  • Resultant: 10 N at 53° north of east. ✓
03
Analysis
[2 marks]

A crate of weight 200 N sits on a ramp inclined at 25° to the horizontal. Resolve its weight into components along and perpendicular to the ramp surface.

  • Component along the ramp (down the slope): 200 sin 25° ≈ 85 N. ✓
  • Component perpendicular to the ramp (into the surface): 200 cos 25° ≈ 181 N. ✓
04
Analysis
[3 marks]

A ball moving at 5.0 m s⁻¹ to the right strikes a wall and rebounds at 5.0 m s⁻¹ to the left. The speed is unchanged, yet there is a change in velocity. Find the magnitude of the change in velocity and explain why it is not zero.

  • Take right as positive: u = +5.0, v = −5.0 m s⁻¹. ✓
  • Δv = v − u = −5.0 − (+5.0) = −10 m s⁻¹, magnitude 10 m s⁻¹ (directed left). ✓
  • Velocity is a vector; the direction reversed, so even with equal speeds the velocity changed by 10 m s⁻¹. ✓
05
Analysis
[2 marks]

Explain, with a sketch in words, why three coplanar forces acting on an object in equilibrium can be represented by a closed triangle.

  • In equilibrium the resultant force is zero. ✓
  • Drawing the three forces nose to tail, a zero resultant means the path returns to its starting point, so the three vectors form a closed triangle. ✓
06
Analysis
[2 marks]

A student claims that adding a 4 N force and a 3 N force always gives 7 N. State when this is true and give the smallest possible magnitude of the resultant of these two forces.

  • The sum 7 N is the resultant only when the two forces point in the same direction (parallel). ✓
  • The smallest magnitude is when they are opposite: 4 − 3 = 1 N. The resultant can be anywhere from 1 N to 7 N depending on the angle. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.