Syllabus Edition

First teaching 2014

Last exams 2024

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Vectors & Scalars (DP IB Physics: SL)

Exam Questions

3 hours45 questions
1
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1 mark

The velocity vectors vX and vY of two cars, X and Y, are shown. 

1-3-q1-sl-easy-mcq-phy

Which arrow represents the direction of the vector vX – vY?

1-3-q1-opt-sl-easy-mcq-phy

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    2
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    1 mark

    Which of the following statements about scalar quantities is incorrect? 

    • Scalar quantities contain a magnitude only

    • Mass is a scalar quantity

    • Scalar quantities contain both magnitude and direction 

    • Speed is a scalar quantity

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    3
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    1 mark

    Which of the following quantities is not a vector? 

    • Acceleration

    • Weight

    • Mass

    • Drag

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    4
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    1 mark

    A vector of magnitude 10 units is shown with respect to a set x and y axes. 

    1-3-q4-sl-easy-mcq-phy

    What is the correct expression for the components of the vector along the x and y axis? 

      Component along the x axis Component along the y axis
    A. 10 cos 76 10 sin 76
    B. 10 cos 76 10 sin 14
    C. 10 sin 76 10 cos 76
    D. 10 sin 76 10 cos 14

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      5
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      1 mark

      A vector P has components Px = 3.0 cm and Py = 4.0 cm. 

      What is the length of the vector P?  

      • 1.0 cm

      • 5.0 cm

      • 7.0 cm

      • 25.0 cm

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      6
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      1 mark

      Three forces act on a body in equilibrium. Which diagram is a possible vector diagram for this situation? 

      1-3-q6-sl-easy-mcq-phy

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        7
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        1 mark

        Three forces act on a body as shown: 

        1-3-q7-sl-easy-mcq-phy

        Which of the following statements is correct? 

        • The body is in equilibrium

        • The force required to bring the body into equilibrium is directed in a north west direction

        • The force required to bring the body into equilibrium is directed in a south east direction

        • There is no resultant force on the body

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        8
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        1 mark

        Which of the following units is used to measure vectors only? 

        • m

        • m s–1

        • s

        • N

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        9
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        1 mark

        Which of the following units is used to measure scalar quantities only? 

        • s

        • m

        • m s–1

        • m s–2

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        10
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        1 mark

        Which of the following statements about vector quantities is incorrect? 

        • Vectors quantities include a magnitude

        • Vector quantities contain a direction

        • Vector quantities are only positive

        • Vector quantities are positive or negative

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        1
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        1 mark

        Velocity is a vector quantity, so can be represented by a vector arrow. Which quantity is represented by the length of its vector arrow?

        • Speed 

        • Magnitude 

        • Acceleration

        • Distance 

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        2
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        1 mark

        Which of the following represents correct vector and scalar quantities?

         

        vectors

        scalars

        A.

        Electric charge

        Weight

        B.

        Impulse

        Current

        C.

        Temperature

        Pressure

        D.

        Time

        Work done

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          3
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          1 mark

          Which of the following represents the correct values of the x-component and y-component of the vector -F ?

          q13_vectors--scalars_ib-sl-physics-mcq

           

          x-component

          y-component

          A.

          F sin θ

          F cos θ

          B.

          F cos θ

          F tan θ

          C.

          F sin θ

          F cos θ

          D.

          F cos θ

          F sin θ

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            4
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            1 mark

            The magnitude of a is 15 N and that of b is 30 N.

            q14_vectors--scalars_ib-sl-physics-mcq

             

             Which of the following represents the correct resultant horizontal and vertical components of the vectors in the diagram?

             

            Horizontal Component

            Vertical Component

            A.

            15square root of 3 – 7.5square root of 2N

            15 – 7.5square root of 2N

            B.

            15square root of 3 – 7.5square root of 2º

            –15 – 7.5square root of 2º

            C.

            15square root of 3 – 7.5square root of 2N

            –15 – 7.5square root of 2N

            D.

            –15 – 7.5 square root of 2N

            15  – 7.5 square root of 2N

              

            You may use the fact that:

            cos(30) = fraction numerator square root of 3 over denominator 2 end fractionand cos(45) = fraction numerator square root of 2 over denominator 2 end fraction

             

            sin(30) = 1 half  and sin(45) = fraction numerator square root of 2 over denominator 2 end fraction

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              5
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              1 mark

              The diagram shows vector p.q15_vectors--scalars_ib-sl-physics-mcq

              In which of the following diagrams is vector p multiplied by a scalar represented?

              q5-1-3m-mcq-ib-hl-vectors-and-scalars

               

                

              • 1 and 4

              • 2 only

              • 2 and 4

              • 1 only

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              6
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              1 mark

              In which of the following diagrams is the addition of vectors x and y represented?

              q16_vectors--scalars_ib-sl-physics-mcqq16_2_vectors--scalars_ib-sl-physics-mcq

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                7
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                1 mark

                In which of the following diagrams is p represented correctly?

                q17_vectors--scalars_ib-sl-physics-mcqq17_2_vectors--scalars_ib-sl-physics-mcq

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                  8
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                  1 mark

                  The arrow represents the vector R.

                  q18_1_vectors--scalars_ib-sl-physics-mcq

                   

                  Which diagram does not represent R as two perpendicular components?

                  q18_2_vectors--scalars_ib-sl-physics-mcq

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                    9
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                    1 mark

                    Three forces act on a body as shown.

                    q19_1_vectors--scalars_ib-sl-physics-mcq

                    Which fourth force is required so that the resultant force is zero?

                    q19_2_vectors--scalars_ib-sl-physics-mcq

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                      10
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                      1 mark

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

                      q20_vectors--scalars_ib-sl-physics-mcq 

                      R is the normal force, W is the weight and F is friction. 

                      Which row correctly labels R and F in terms of mass m and acceleration due to gravity g.

                       

                       

                      R

                      F

                      A.

                      mg

                      mg

                      B.

                      mg cos θ

                      0

                      C.

                      mg sin θ

                      mg cos θ

                      D.

                      mg cos θ

                      mg sin θ

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                        1
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                        1 mark

                        A pilot wishes to set her plane on a course such that it flies directly west of its starting point. She must take into account the strong northerly wind, meaning that she is flying in a wind which originates in the north and blows in a southward direction. 

                        On which course should the plane be directed? 

                        1-3-sl-mcq-hard-q1-phy

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                          2
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                          1 mark

                          A positron is in the effect of two electric fields, shown measured in arbitrary units. 

                          1-3-sl-mcq-hard-q2-phy

                          What is the magnitude of the resultant field strength on the positron? 

                          You may use any of the following results:

                          • cosine rule: a2b2c2 – 2bc cos A
                          • cos 60° = 0.5
                          • cos 120° = –0.5
                          • square root of 13 V m–1

                          • 6 V m–1

                          • 13 V m–1

                          • square root of 37 V m–1

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                          3
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                          1 mark

                          A drifting spider of mass 50 g hangs on its web from point P on a ceiling. It is being displaced at an angle θ to the vertical by a gentle breeze equivalent to 0.2 N. 

                          1-3-sl-mcq-hard-q3-phy

                          What is the magnitude of the angle θ?

                          You may assume g = 10 m s–2

                          • sin–1 (0.4)

                          • cos–1 (2.5)

                          • tan–1 (0.4)

                          • tan–1 (2.5)

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                          4
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                          1 mark

                          A horizontal force F  accelerates a body of mass m up a rough plane inclined at an angle θ to the horizontal. 

                          sl-mcq-1-3-hard-q4

                          Which expression describes the magnitude of the resultant force on the body?  

                          • cos θ – mg sin θ

                          • F cos θ – mg (sin θ – μd cos θ)

                          • F(cos θ – μd sin θ) – mg (sin θ – μd cos θ)

                          • mg (sin θ – μd cos θ) + F(cos θ – μd sin θ)

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                          5
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                          1 mark

                          A box rests on an inclined plane. 

                          1-3-sl-mcq-hard-q5-phy

                          Which of the following statements is correct if the incline becomes less steep? 

                          • Vector Y decreases

                          • Vector Y increases

                          • Vector X increases

                          • Vector Z increases

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                          6
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                          1 mark

                          The following processes are given: 

                          1. The friction required to bring a car to a complete halt. 
                          2. The effort required to nail a hammer into wood. 
                          3. The heat required to cook. 

                          Which of the processes is a scalar quantity? 

                          • I and II only

                          • III only

                          • II and III only

                          • I, II and III

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                          7
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                          1 mark

                          Alice sits on the platform of a train station, observing the trains as they move past, from left to right, at constant velocity. 

                          Bob is sat in one particular train carriage, and throws a tennis ball vertically upward, catching it as it comes back down.

                          Which diagram best represents the trajectory of the tennis ball relative to Alice? (Note: this is the path the ball will follow relative to Alice's position, not what she will see.)

                          1-3-sl-mcq-hard-q7-phy

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                            8
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                            1 mark

                            In some models of quantum theory, photons of light take infinitely many paths between two points P and Q in space. Three such paths are shown. 

                            1-3-sl-mcq-hard-q8_1-phy

                            We can associate a mathematical object called a phasor to each of these unique paths. A phasor can be thought of as a spinning vector. For example, when a photon leaves its source P, its associated phasor begins rotating like a clock, until the photon is detected at Q. At this instant, the phasor stops rotating.

                            In this way, different paths are represented by different phasors. The phasor's final orientation depends on the time taken by the photon to travel between P and Q.

                            Some example final positions of phasors for different paths are shown: 

                            1-3-sl-mcq-hard-q8_2-phy

                            Quantum theory requires that phasors for every possible path are used to calculate the probability of detecting a photon at Q.  More specifically, the probability of detecting a photon at Q is proportional to the square of the resultant phasor amplitude at Q. 

                            Which diagram best represents the resultant phasor amplitude at Q if Q is the dark fringe of an interference pattern? 

                            1-3-sl-mcq-hard-q8_3-phy

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                              9
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                              1 mark

                              A car drives from its base camp, at position X, to lodge P, 40 km away, at a bearing of 030° from X. After dropping off supplies it continues to lodge Q, which is 50 km away and at a bearing of 330° from P. 

                              What is the distance between base camp and lodge Q? 

                              You may use one, none or some of the following values for cosines in your calculation:

                              cos(60) = + 0.5

                              cos(90) = 0

                              cos(120) = − 0.5

                              • 5 square root of 21km

                              • 5 square root of 61km

                              • 10 square root of 21km

                              • 10 square root of 61km

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                              10
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                              1 mark

                              A vector field is a mathematical description which assigns a vector to every point in a subset of space. 

                              1-3-sl-mcq-hard-q10-phy

                              Which of the following vector fields could not be represented by the image shown? 

                              • A gravitational vector field

                              • An electric vector field

                              • A velocity vector field

                              • A magnetic vector field 

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