A Level Physics 1.4 Scalars and Vectors MCQs – 30 Practice Questions with Answers (Cambridge 9702)

Free practice MCQs for Cambridge International AS & A Level Physics (9702), Section 1.4 Scalars and Vectors. Test yourself on scalar and vector quantities, adding vectors, and resolving vectors into components – every question has a fully worked answer.

Formula recap: Resultant of two perpendicular vectors: R = √(A2 + B2), with tan θ = opposite / adjacent. Components of a vector F at angle θ to the horizontal: Fx = F cos θ and Fy = F sin θ. Keep the full set of equations handy in our A Level Physics Formula Sheet.

Scalar & Vector Quantities

Q1. Which of the following quantities is a vector?

  • (A) speed
  • (B) mass
  • (C) temperature
  • (D) velocity
Show Answer

Answer: D – A vector has both magnitude and direction. Velocity is displacement per unit time in a stated direction, so it is a vector. Speed, mass and temperature have magnitude only, so they are scalars.

Q2. Which row contains only scalar quantities?

  • (A) distance, energy, temperature, pressure
  • (B) displacement, energy, mass, pressure
  • (C) force, momentum, temperature, distance
  • (D) velocity, acceleration, energy, mass
Show Answer

Answer: A – Distance, energy, temperature and pressure are all fully described by magnitude alone. Every other row contains at least one vector: displacement, force, momentum, velocity and acceleration all need a direction.

Q3. An athlete runs exactly one complete lap of a 400 m track and finishes at the starting point. What is the athlete’s displacement for the lap?

  • (A) 400 m
  • (B) 200 m
  • (C) 0 m
  • (D) 800 m
Show Answer

Answer: C – Displacement is the straight-line change of position from start to finish. The athlete ends where they started, so the displacement is zero, even though the distance travelled is 400 m.

Q4. A car travels 60 km north and then returns 60 km south along the same road, taking 2.0 hours in total. What is the car’s average velocity for the whole journey?

  • (A) 60 km/h north
  • (B) 0 km/h
  • (C) 30 km/h north
  • (D) 15 km/h south
Show Answer

Answer: B – Average velocity = total displacement / total time. The car returns to its start, so the total displacement is zero and the average velocity is 0 km/h. Its average speed, by contrast, is 120 km / 2.0 h = 60 km/h, which is not zero.

Q5. Which of the following is NOT a vector quantity?

  • (A) force
  • (B) momentum
  • (C) acceleration
  • (D) pressure
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Answer: D – Pressure is force per unit area and has no direction of its own, so it is a scalar. Force, momentum and acceleration all act in a particular direction, so they are vectors.

Q6. Which statement best defines displacement?

  • (A) The total length of the path travelled by an object
  • (B) The straight-line distance from the starting point to the finishing point, in a specified direction
  • (C) The distance travelled divided by the time taken
  • (D) The change in speed of an object in a given time
Show Answer

Answer: B – Displacement is a vector: it measures how far the final position is from the initial position along a straight line, together with the direction. Option (A) defines distance, a scalar.

Q7. A vector quantity is drawn as an arrow. What do the length and the direction of the arrow represent?

  • (A) Length: the speed of the object; direction: the path taken
  • (B) Length: the time taken; direction: the magnitude of the quantity
  • (C) Length: the magnitude of the quantity; direction: the direction of the quantity
  • (D) Length: the direction of the quantity; direction: the magnitude of the quantity
Show Answer

Answer: C – In a vector diagram the arrow is drawn to scale: its length is proportional to the magnitude of the vector, and it points in the direction in which the vector acts.

Q8. Which pair consists of two vector quantities?

  • (A) momentum and weight
  • (B) energy and momentum
  • (C) weight and mass
  • (D) power and force
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Answer: A – Momentum (mass × velocity) points in the direction of motion, and weight is a force acting towards the centre of the Earth. Energy, mass and power are scalars, so the other pairs each contain only one vector.

Q9. Which statement about speed and velocity is correct?

  • (A) Speed and velocity are always equal in magnitude
  • (B) Velocity is a scalar and speed is a vector
  • (C) An object moving in a circle at constant speed has a constant velocity
  • (D) An object’s velocity can change even when its speed stays constant
Show Answer

Answer: D – Velocity depends on direction as well as magnitude. An object moving in a circle at constant speed is continually changing direction, so its velocity is continually changing (it is accelerating towards the centre).

Q10. Taking the eastward direction as positive, a cyclist has a velocity of −15 m/s. What does this mean?

  • (A) The cyclist is travelling east at 15 m/s and slowing down
  • (B) The cyclist is travelling west at 15 m/s
  • (C) The cyclist is travelling east at −15 m/s below ground level
  • (D) The cyclist is stationary and facing west
Show Answer

Answer: B – For a vector written with a sign, the sign shows direction along the chosen axis. A negative velocity with east defined as positive means motion in the opposite direction: 15 m/s towards the west.

Adding Vectors

Q11. Two forces act on an object along the same line: 9 N towards the east and 4 N towards the west. What is the resultant force?

  • (A) 13 N towards the east
  • (B) 5 N towards the west
  • (C) 5 N towards the east
  • (D) 13 N towards the west
Show Answer

Answer: C – For collinear vectors, add with signs. Taking east as positive: +9 + (−4) = +5 N, so the resultant is 5 N towards the east. (Adding 9 + 4 = 13 N ignores the opposite directions.)

Q12. Two forces of 30 N and 40 N act on a point at right angles to each other. What is the magnitude of the resultant force?

  • (A) 50 N
  • (B) 70 N
  • (C) 10 N
  • (D) 58 N
Show Answer

Answer: A – The two forces form the sides of a right-angled triangle (a 3-4-5 triangle scaled by 10). Resultant = √(302 + 402) = √(900 + 1600) = √2500 = 50 N.

Q13. A boat moves through the water at 6.0 m/s towards the east. A current carries it towards the north at 8.0 m/s. At what angle north of east is the boat’s resultant velocity directed?

  • (A) 37°
  • (B) 45°
  • (C) 90°
  • (D) 53°
Show Answer

Answer: D – The components are 6.0 m/s east and 8.0 m/s north. tan θ = opposite / adjacent = 8.0 / 6.0 = 1.33, so θ = tan−1(1.33) = 53° north of east. (The magnitude is √(62 + 82) = 10 m/s, a 6-8-10 triangle.)

Q14. Two forces, each of magnitude 10 N, act on an object at 90° to each other. What is the magnitude of the resultant?

  • (A) 20 N
  • (B) 14 N
  • (C) 0 N
  • (D) 10 N
Show Answer

Answer: B – Resultant = √(102 + 102) = √200 = 10√2 = 14 N. Two equal vectors at 90° always give a resultant of F√2 at 45° between them.

Q15. Two vectors have magnitudes 8 N and 6 N. What are the maximum and minimum possible magnitudes of their resultant?

  • (A) Maximum 14 N, minimum 10 N
  • (B) Maximum 48 N, minimum 2 N
  • (C) Maximum 14 N, minimum 2 N
  • (D) Maximum 10 N, minimum 2 N
Show Answer

Answer: C – The resultant is largest when the two vectors point in the same direction: 8 + 6 = 14 N. It is smallest when they point in opposite directions: 8 − 6 = 2 N. Any angle between 0° and 180° gives a resultant between these limits.

Q16. Which statement correctly describes the parallelogram law of vector addition?

  • (A) Two vectors are placed tail-to-tail and the resultant is the longer of the two sides
  • (B) The resultant of two vectors is always the arithmetic sum of their magnitudes
  • (C) Two vectors are added by placing the tail of the second at the head of the first
  • (D) Two vectors drawn from a point form adjacent sides of a parallelogram, and the resultant is the diagonal from that point
Show Answer

Answer: D – In the parallelogram law, both vectors are drawn from the same point as adjacent sides of a parallelogram; the diagonal through that point gives the resultant in magnitude and direction. Option (C) describes the triangle law, which gives the same answer drawn differently.

Q17. Forces of 5 N east and 12 N north act on a point. A single equilibrant force is added so that the point is in equilibrium. What is the equilibrant?

  • (A) 13 N in the direction of the resultant
  • (B) 13 N in the opposite direction to the resultant
  • (C) 17 N towards the south-west
  • (D) 7 N towards the west
Show Answer

Answer: B – The resultant is √(52 + 122) = √169 = 13 N (a 5-12-13 triangle). The equilibrant must cancel it exactly, so it is equal in magnitude (13 N) and opposite in direction to the resultant.

Q18. Taking east as positive, a car’s velocity changes from +25 m/s to −15 m/s. What is the change in velocity?

  • (A) 40 m/s towards the west
  • (B) 10 m/s towards the west
  • (C) 40 m/s towards the east
  • (D) 10 m/s towards the east
Show Answer

Answer: A – Change in velocity = final − initial = (−15) − (+25) = −40 m/s. The negative sign means the change is directed west, with magnitude 40 m/s. Simply subtracting the speeds (25 − 15 = 10) ignores the reversal of direction.

Q19. A resultant is formed from a component of 5.0 m/s towards the east and a component of 12 m/s towards the north. At what angle to the east is the resultant directed?

  • (A) 23°
  • (B) 45°
  • (C) 67°
  • (D) 53°
Show Answer

Answer: C – tan θ = north component / east component = 12 / 5.0 = 2.4, so θ = tan−1(2.4) = 67° north of east. (The resultant magnitude is √(25 + 144) = 13 m/s.)

Q20. Three forces act on an object and the object remains in equilibrium. When the three force vectors are drawn head-to-tail in any order, what do they form?

  • (A) A straight line
  • (B) An open triangle
  • (C) A right-angled triangle only
  • (D) A closed triangle
Show Answer

Answer: D – In equilibrium the resultant force is zero. Drawing the vectors head-to-tail, the final head meets the first tail, so the vectors form a closed triangle. This is the triangle-of-forces condition for equilibrium.


Resolving Vectors into Components

Q21. A force of 50 N acts at 30° above the horizontal. What is the horizontal component of the force?

  • (A) 43 N
  • (B) 25 N
  • (C) 29 N
  • (D) 50 N
Show Answer

Answer: A – The angle is measured from the horizontal, so the horizontal component is adjacent to the angle: Fx = F cos θ = 50 × cos 30° = 50 × 0.866 = 43 N. (25 N is the vertical component, F sin 30°.)

Q22. A force of 50 N acts at 30° above the horizontal. What is the vertical component of the force?

  • (A) 43 N
  • (B) 29 N
  • (C) 25 N
  • (D) 87 N
Show Answer

Answer: C – Fy = F sin θ = 50 × sin 30° = 50 × 0.50 = 25 N. Check: √(432 + 252) = 50 N, as required.

Q23. A velocity has a horizontal component of 9.0 m/s and a vertical component of 12 m/s. What is the magnitude of the velocity?

  • (A) 21 m/s
  • (B) 3.0 m/s
  • (C) 10.8 m/s
  • (D) 15 m/s
Show Answer

Answer: D – The components are perpendicular, so v = √(9.02 + 122) = √(81 + 144) = √225 = 15 m/s (a 9-12-15 triangle).

Q24. A ball is projected at 24 m/s at an angle of 60° above the horizontal. What is the horizontal component of its initial velocity?

  • (A) 21 m/s
  • (B) 12 m/s
  • (C) 24 m/s
  • (D) 14 m/s
Show Answer

Answer: B – ux = u cos θ = 24 × cos 60° = 24 × 0.50 = 12 m/s. This horizontal component stays constant throughout the flight (ignoring air resistance).

Q25. The ball in Q24 is projected at 24 m/s at 60° above the horizontal. What is the vertical component of its initial velocity?

  • (A) 12 m/s
  • (B) 24 m/s
  • (C) 21 m/s
  • (D) 42 m/s
Show Answer

Answer: C – uy = u sin θ = 24 × sin 60° = 24 × 0.866 = 20.8, about 21 m/s. It is this component that gravity then changes during the flight.

Q26. A block of weight 200 N rests on a slope inclined at 30° to the horizontal. What is the component of the weight acting down the slope?

  • (A) 100 N
  • (B) 173 N
  • (C) 200 N
  • (D) 50 N
Show Answer

Answer: A – The component of the weight parallel to the slope is mg sin θ, where θ is the slope angle: 200 × sin 30° = 200 × 0.50 = 100 N. (173 N is the component perpendicular to the slope, mg cos θ.)

Q27. Two forces act on a point: 20 N horizontally, and 20 N at 60° above the horizontal. By resolving both forces into horizontal and vertical components, what is the magnitude of the resultant?

  • (A) 40 N
  • (B) 28 N
  • (C) 45 N
  • (D) 35 N
Show Answer

Answer: D – Resolve the 20 N force at 60°: horizontal = 20 cos 60° = 10 N; vertical = 20 sin 60° = 17.3 N. Totals: horizontal = 20 + 10 = 30 N; vertical = 17.3 N. Resultant = √(302 + 17.32) = √(900 + 300) = √1200 = 34.6, about 35 N.

Q28. A sledge is pulled by a rope exerting a force of 120 N at 45° above the horizontal. What is the horizontal component of the pull?

  • (A) 85 N
  • (B) 60 N
  • (C) 120 N
  • (D) 170 N
Show Answer

Answer: A – Horizontal component = 120 × cos 45° = 120 × 0.707 = 84.9, about 85 N. At 45° the vertical component is the same, 85 N, since sin 45° = cos 45°.

Q29. A force of 100 N acts at 60° above the horizontal. What is the vertical component of the force?

  • (A) 50 N
  • (B) 58 N
  • (C) 87 N
  • (D) 100 N
Show Answer

Answer: C – Fy = F sin θ = 100 × sin 60° = 100 × 0.866 = 86.6, about 87 N. (50 N is the horizontal component, 100 cos 60°.)

Q30. A block of weight 200 N rests on a slope inclined at 30° to the horizontal. What is the component of the weight acting perpendicular to the slope (the component balanced by the normal contact force)?

  • (A) 100 N
  • (B) 173 N
  • (C) 200 N
  • (D) 0 N
Show Answer

Answer: B – The component perpendicular to the slope is mg cos θ = 200 × cos 30° = 200 × 0.866 = 173 N. This is balanced by the normal reaction of the slope; the other component, mg sin θ = 100 N, acts down the slope.

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