Syllabus Edition

First teaching 2023

First exams 2025

|

Scalars & Vectors (CIE A Level Physics)

Exam Questions

1 hour22 questions
1a
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2 marks

Distinguish between scalar and vector quantities.

1b
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6 marks
(i)

Energy is a scalar quantity. State three other scalar quantities.

[3]
(ii)
Force is a vector quantity. State three other vector quantities.
[3]
1c
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4 marks

Fig. 1.1 shows a block at rest on a slope.

Three forces, weight W, normal contact force N and the frictional force F act on the block. The forces are in equilibrium.

1-1-1c-e-1-1-e-box-slope-vector-combine-cie-ial-sq

(i)
Explain what is meant by 'the forces are in equilibrium'.
[2]
(ii)
Complete the vector triangle in Fig. 1.2. Label the missing vector and the angle between W and N.
 

1-1-1c-e-1-1-e-box-slope-vector-triangle-cie-ial-sq

[2]

1d
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4 marks

The frictional force has a magnitude of 60 N.

By resolving the vector, calculate the component of the force that acts

 
(i)
horizontally
[2]
(ii)
vertically.
[2]

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2a
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2 marks

State the definition of a vector quantity. 

2b
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3 marks

A list of vector quantities and their SI unit is given.

Quantity SI unit
Temperature  
  kg m s-1
Mass  

Complete the information missing from the table. 

2c
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2 marks

A person cycles along a path every day, from their front garden at X to a bench by the nearby lake at Y, as shown in Fig. 1.1.

1-3-q1c-easy-sq-sl-phy

Fig. 1.1

(i)
Sketch a line on the image that would indicate the distance travelled by the person between X and Y. Label this distance d
[1]
(ii)
State whether the distance travelled d by the person is greater than, equal to, or less than their displacement between X and Y.
[1]

 

2d
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2 marks

The person continues their journey and walks along the same path back home, from Y to X. The total distance for their complete journey which was logged by their smartwatch is 4.3 km. State and explain what the total displacement for their journey is. 

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3a
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2 marks

A small cannon fires a projectile at an angle of 22° to the horizontal with an initial velocity v

1-3-q4a-easy-sq-sl-phy

Calculate the vertical component of velocity if its initial velocity has a magnitude of v = 15 m s–1

3b
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1 mark

State the direction of the horizontal component of velocity. 

3c
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2 marks

The cannon fires a second projectile. The initial horizontal component of velocity is 8.4 m s-1 and the initial vertical component of velocity is 5.8 m s-1.

Calculate the initial velocity, v2, of the second projectile.

3d
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2 marks

Calculate the angle to the horizontal that the second projectile was fired at.

[2]

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1a
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7 marks

The relationship can be used to model a spherical raindrop falling vertically in the air.

Fig 1.1 shows the forces acting on the raindrop as it accelerates downwards.

1-1-3c-m-1-1-raindrop-sphere-vector-forces-cie-ial-sq

The raindrop has a radius of 1.5 mm and falls at a velocity of 3.5 m s−1. The constant k has a magnitude of 0.0124 in air.

Other than the resistive force F described in (b), two other forces, X and Y, act on the raindrop drop as it falls through the air. 

(i)
State the names of forces X and Y.
[2]

  

(ii)
Calculate the magnitude of the resistive force F in µN.
[2]
 
(iii)
Force X has a value of 137 µN and force Y has a value of 0.18 µN.
 
Using Fig. 1.1, determine the magnitude and direction of the resultant force on the raindrop.
[3]
1b
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3 marks

On a windy day, the resultant force on the raindrop is 105 µN at an angle of θ to the vertical as shown in Fig. 1.2. 

1-1-3d-m-1-1-raindrop-sphere-vector-angle-cie-ial-sq

Use your answer to (c)iii to show that the angle θ between the resultant and the vertical is about 47°.

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2a
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2 marks
(i)
State the difference between a scalar quantity and a vector quantity.
[1]
(ii)
Underline all the vectors in the list below.
 
power           length           density           velocity           momentum
[1]
2b
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4 marks

Two gusts of wind exert forces of magnitude 5.5 N and 11.9 N on a wind turbine at a point O. Both forces act away from point O and the angle between them is 30°.

Fig. 1.1 shows two lines at an angle of 30° to one another.

 

1-1-4b-m-1-1-vector-force-triangle-cie-ial-sq

Fig. 1.1

 

On Fig. 1.1, draw a vector diagram to determine the magnitude of the resultant of the two forces.

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3a
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4 marks

Fig. 1.1 shows a 2 tonne wrecking ball being used on a demolition site. 

1-1-5a-m-1-1-wrecking-ball-resolving-vectors-cie-ial-sq

The ball is suspended from a cable which makes an angle θ with the vertical. The ball is pulled into the position shown by a rope that is kept horizontal. The tension in the rope is 6400 N.

Write expressions for tension T using

(i)
the vertical component of the tension in the cable
[2]
(ii)
the horizontal component of the tension in the cable. 
[2]
3b
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4 marks

Determine

(i)
the angle θ the cable makes with the vertical
[2]
(ii)
the magnitude of the tension T in the cable
[2]
3c
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3 marks

On the same demolition site, there is a uniform beam supported by two light cables, AB and AC, which are attached to a single steel cable from a crane, as shown in Fig. 1.2.

The beam is stationary and in equilibrium.

q5c_vectors--scalars-in-physics_ib-sl-physics-sq

Fig. 1.2

Draw the vector triangle for this situation labelling the tension in both cables and the weight of the beam. 

3d
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2 marks

The tension in the cable AB is 9 N and the tension in the cable AC is 12 N.

Calculate the resultant force required in the beam BC to keep the system in equilibrium.

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