Scalars & Vectors (AQA AS Physics)

Exam Questions

3 hours45 questions
11 mark

Which statement regarding vectors and scalars is correct?

  • A scalar is a quantity which only has direction

  • A vector is a quantity which only has direction

  • A scalar is a quantity which only has magnitude

  • A vector is a quantity which only has magnitude

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21 mark

Which of the following is a scalar quantity?

  • Acceleration

  • Momentum

  • Density

  • Force

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31 mark

Which of the following is a vector quantity?

  • Direction

  • Speed

  • Energy

  • Displacement 

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41 mark

Velocity is a vector quantity, and so can be represented by a vector arrow.

Which quantity is represented by the length of its vector arrow?

  • Acceleration

  • Direction

  • Speed

  • Displacement 

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51 mark

Two vectors are drawn at right angles to each other

q5_scalars-_-vectors_aqa-as-physics-mcq

Which equation can be used to find the magnitude of the resultant vector, R?

  • R = a2 + b2

  • Rsquare root of a squared space plus space b squared end root

  • R = square root of a plus b end root

  • R = a + b

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61 mark

The diagram shows two forces at right angles to each other.

q6_scalars-_-vectors_aqa-as-physics-mcq

What is the magnitude resultant force, R?

  • 12 N

  • 149 N

  • 4 N

  • 17 N

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71 mark

Velocity vectors can be resolved into vertical and horizontal components, each at 90º to each other.

The diagram shows the vertical and horizontal components for a velocity vector, v. 

q7_scalars-_-vectors_aqa-as-physics-mcq

What is the direction of the velocity vector with respect to the horizontal, given by ?

  • 33 o to the horizontal

  • 56 o to the horizontal

  • 1.5 o to the horizontal

  • 42 o to the horizontal

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81 mark

A cyclist travels a distance of 12 km due west and 18 km due south.

What is the magnitude of their overall displacement?

  • 5 km

  • 30 km

  • 22 km

  • 468 km

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91 mark

Vector F is inclined to the horizontal at angle θ

q9_scalars-_-vectors_aqa-as-physics-mcq

What is the correct expression for the vertical component of vector F?

  • F sin θ

  • F cos θ

  • θ sin F

  • θ cos F

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101 mark

A rectangular object sits at rest on a plane inclined at angle θ  to the horizontal

q10_scalars-_-vectors_aqa-as-physics-mcq

Which line, A to D in the table below correctly labels each force J, K and L?

 

J

K

L

A

friction

weight

reaction force

B

reaction force

mass

friction

C

friction

mass

reaction force

D

reaction force

weight

friction

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    11 mark

    The arrow represents the vector R.

    q11-1_scalars-_-vectors_aqa-as-physics-mcq

    Which diagram does not represent R as two perpendicular components?

    q11-2_scalars-_-vectors_aqa-as-physics-mcq

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      21 mark

      The speed of an aeroplane in still air is 200 km h–1. The wind blows from the west at a speed of 85.0 km h–1.

      In which direction must the pilot steer the aeroplane in order to fly due north?

      • 23.0° east of north

      • 23.0° west of north

      • 25.2° east of north

      • 25.2° west of north

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      31 mark

      Vectors P and Q are drawn to scale.

      q13_scalars-_-vectors_aqa-as-physics-mcq

      Which diagram represents the vector (PQ)?

      q13-2_scalars-_-vectors_aqa-as-physics-mcq

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        41 mark

        A vector has magnitude R and perpendicular components P and Q, as shown in the diagram.

        q14_scalars-_-vectors_aqa-as-physics-mcq

        Which row correctly describes the perpendicular components?

         

        vertical component

        horizontal component

        A Q

        sin θ

        B

        R cos θ

        P
        C

        R cos θ

        R sin θ

        D

        R sin θ

        R cos θ

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          51 mark

          The table shows the x-component and y-component of four force vectors.

          Which force vector has the largest magnitude?

           

          x-component / N

          y-component / N

          A 2 9

          B

          3 8

          C

          4 7
          D 5 6

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            61 mark

            Coplanar forces of 13 N, 12 N and 5 N act on an object. Which force, in N, could not possibly be the resultant of these forces?

            • 0

            • 6

            • 30

            • 46

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            71 mark

            Square objects A, B, C and D are each acted on by three forces.

            Which one of the objects is in equilibrium?

            q17_scalars-_-vectors_aqa-as-physics-mcq

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              81 mark

              A block has a weight of 14 N and sits on a ramp inclined at 27o to the horizontal.

              q18_scalars-_-vectors_aqa-as-physics-mcq

              What is the component of weight which is acting down the ramp?

              • 14 N

              • 12 N

              • 6.5 N

              • 6.4 N

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              91 mark

              A pendulum is oscillating from a fixed point. The bob at the end has weight 2.0 N.

              At a given instant the angle of the string is inclined at 23 o to the vertical.

              q19_scalars-_-vectors_aqa-as-physics-mcq

              What is the component of weight which is parallel to the string?

              • 1.8 N

              • 0.78 N

              • 0.80 N

              • 23 N

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              101 mark

              Two forces act on a block. There is a downwards force of 45 N and a horizontal force of 27 N to the right.

              Which line, A to D, in the table below correctly gives the magnitude resultant force and the angle it makes to the horizontal?

               

              Magnitude of resultant force

              Angle / o

              A

              8.5 N

              37 o

              B

              52 N

              59 o

              C

              2800 N

              53 o

              D

              72 N

              31 o

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                11 mark

                A swimmer is travelling at 1.2 m s–1. They are in a river with a drift current of 0.35 m s–1 due south.

                At what angle, measured clockwise from due north, must the swimmer travel in order to travel due east, relative to a stationary observer?

                • 16 o

                • 74 o

                • 73 o

                • 17 o

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                21 mark

                A gymnast of mass 65 kg is holding himself stationary on the rings.

                q22_scalars-_-vectors_aqa-as-physics-mcq

                The angle between the gymnast’s arms and the ropes is 68 o.

                What is the tension, T, in each rope?

                • 340 N

                • 850 N

                • 690 N

                • 1700 N

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                31 mark

                A punching bag is suspended from a light, in extensible rope, and is pushed with a force of 300 N to the left, making a stationary angle between the supporting rope and the vertical of 23o.

                Calculate the mass of the bag.

                • 0.18 kg

                • 710 kg

                • 78 kg

                • 72 kg

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                41 mark

                A uniform rectangular block sits on a rough slope inclined at 36 o to the horizontal. The block is at rest and the static friction is 41 N as shown. 

                q24_scalars-_-vectors_aqa-as-physics-mcq

                When the mass of the block is increased by 23% the block begins to accelerate down the slope.

                What is the new mass of the block?

                • 6.4 kg

                • 8.7 kg

                • 1.6 kg

                • 86 kg

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                51 mark

                A barge travels straight along a canal at a steady speed. A horse is towing the barge, and a person walks on the other bank holding a rope under a tension of 20 N.

                q25_scalars-_-vectors_aqa-as-physics-mcq

                The drag experienced by the barge is 50 N.

                Which line, A to D, in the table below correctly gives the magnitude of the tension caused by the towing horse and the angle which the horse’s rope makes to the direction of motion?

                 

                Magnitude of tension

                Angle / o to direction of motion

                A 30 N 68 o
                B 8.4 N 24 o
                C 70 N 66 o
                D 54 N 22 o

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                  61 mark

                  The speed of a walker is denoted by v m s–1. When walking up a hill inclined at angle  θ° to the horizontal, the walker travels a distance of s m. The walker travels for a time of t s.

                  Which of the following is not a correct expression for the height, h, obtained by the walker over their journey?

                  • s over v square root of v squared space sin squared space theta end root

                  • vt sin θ

                  • square root of left parenthesis v t right parenthesis squared space sin to the power of 2 space end exponent theta end root

                  • tsquare root of sin to the power of 2 space end exponent theta end root

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                  71 mark

                  A uniform object of mass, m, sits at rest on a slope inclined at  θ° to the horizontal.

                  The magnitude of friction is given by F = μR where R is the normal reaction force and μ is a constant called the coefficient of friction.

                  Which of the following is not a possible expression for μ?

                  • fraction numerator sin blank theta blank over denominator cos blank theta blank end fraction

                  • tan θ

                  • fraction numerator s i n blank theta blank over denominator W R end fraction

                  • fraction numerator F over denominator W space cos space theta blank end fraction

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                  81 mark

                  Three newtonmeters are attached to a board in fixed positions using nails. Strings are attached to each newtonmeter under tension at point P. One of the strings is horizontal.

                  The values on two of the newtonmeters are shown in the diagram below.

                  q28_scalars-_-vectors_aqa-as-physics-mcq

                  Which line, A to D, in the table below, gives the magnitude of force F on the third newtonmeter and the angle, θ , between F and the horizontal?

                   

                  Magnitude of force F/ N

                  Angle/ o

                  A

                  8.4

                  47

                  B

                  9.1

                  43

                  C

                  6.2

                  42

                  D

                  7.7

                  53

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                    91 mark

                    The force experienced by two charged particles can be given by Coulomb’s Law

                    F = fraction numerator q subscript 1 q subscript 2 over denominator 4 pi epsilon subscript 0 r squared end fraction

                    Where F is the electrostatic force between them, q1 and q2 is the charge of each particle, r is the radial distance between them, and 4 pi epsilon subscript 0 is a constant with a value of 8.85 × 10–12 F m–1.

                    Two identically charged conducting spheres of mass 4.5 × 10–3 kg are suspended in equilibrium by a non-conducting thread in the arrangement shown in the diagram.

                    q29_scalars-_-vectors_aqa-as-physics-mcq

                    The distance, r, between the centre of each sphere is 0.25 m. The charge on each sphere is 68 nC.

                    What is the tension, T, in one of the threads?

                    • 0.0020 N

                    • 0.0525 N

                    • 0.0449 N

                    • 0.0433 N

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                    101 mark

                    A uniform object of mass, m1, sits at rest on a slope inclined at 45 o to the horizontal. The object is held in place by the tension in a rope which passes over a frictionless pulley and is attached to a free-hanging mass, m2.

                    q30_scalars-_-vectors_aqa-as-physics-mcq

                    The mass of m2 is 1kg. The mass of m1 is unknown.

                    If the angle of the slope is increased to 60 o then m1 will begin to slide down the slope. When the angle of the slope is decreased to 30 o then m1 will start to move up the slope.

                    The magnitude of friction F is given by F = μR where R is the normal reaction force and μ is a constant called the coefficient of friction.

                    Which line, A to D, in the table below, gives the value of m1 and the value of μ?

                     

                    Mass / kg

                     μ

                    A

                    0.73

                    -1.01

                    B

                    1.37

                    0.27

                    C

                    1.37

                    -0.27

                    D

                    0.73

                    1.01

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