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Grade 12 Physics entrance exam, 2010 E.C. (2018)

Real questions from the Grade 12 university entrance exam in Physics, as students sat it in 2010 E.C. Every question comes with the correct answer and a worked explanation.

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  • Natural science stream

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  • 2010 E.C. (2018)

    Exam year

  • 41 questions with answers

    In this set

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Question 1

Four vectors are listed below A⃗=[410]\vec{A} = \begin{bmatrix} 4 \\ 10 \end{bmatrix}. B⃗=[2−5]\vec{B} = \begin{bmatrix} 2 \\ -5 \end{bmatrix}, C⃗=[−615]\vec{C} = \begin{bmatrix} -6 \\ 15 \end{bmatrix}, D⃗=[15−6]\vec{D} = \begin{bmatrix} 15 \\ -6 \end{bmatrix}, Which pair of the vectors is orthogonal?

  1. A.A⃗\vec{A} and D⃗\vec{D}
  2. B.B⃗\vec{B} and C⃗\vec{C}
  3. C.C⃗\vec{C} and D⃗\vec{D}
  4. D.A⃗\vec{A} and B⃗\vec{B}
Show the answer and explanation

Answer: A A⃗\vec{A} and D⃗\vec{D}

Why

Two vectors are orthogonal if their dot product equals zero. Calculating the dot product for A⃗\vec{A} and D⃗\vec{D} gives (4)(15)+(10)(−6)=60−60=0(4)(15) + (10)(-6) = 60 - 60 = 0, so they are orthogonal.

Question 2

A race car is moving at a constant speed of 35m/s . A security car was moving at a speed of 5m/s as the race car passes by it and was accelerating at constant rate of 5 m/s2\mathrm{m/s^2}. What was the speed of the security car when it took over the race car ?

  1. A.35m/s
  2. B.60m/s
  3. C.5m/s
  4. D.65m/s
Show the answer and explanation

Answer: D 65m/s

Why

Equating the positions of the race car and security car: 35t=5t+12(5)t235t = 5t + \frac{1}{2}(5)t^2, which simplifies to 2.5t2=30t2.5t^2 = 30t, giving t=12 st = 12\text{ s}. The final speed of the security car is v=v0+at=5+5(12)=65 m/sv = v_0 + at = 5 + 5(12) = 65\text{ m/s}.

Question 3

A car start moving from rest and its motion on a straight line is shown in the figure below. What is the average velocity of the car within the first 6 seconds? [Figure: Hand-drawn velocity-time graph. Vertical axis labelled v (m/s) with tick marks at 2, 4, 6, 8, 10 and 12; horizontal axis labelled t(s) with tick marks at 2, 4, 6 and 8. The trace consists of three straight segments: a line rising from the origin to a point labelled "2, 6" (t = 2 s, v = 6 m/s); a horizontal segment from that point to a point labelled "4, 6" (t = 4 s, v = 6 m/s); then a line rising from there to a point labelled "6, 10" (t = 6 s, v = 10 m/s), where the trace ends.]

  1. A.5.67m/s
  2. B.1.67 m/s
  3. C.5 m/s
  4. D.6 m/s
Show the answer and explanation

Answer: A 5.67m/s

Why

The total displacement is the area under the v-tv\text{-}t graph: Area 1 is 12(2)(6)=6 m\frac{1}{2}(2)(6) = 6\text{ m}, Area 2 is (4−2)(6)=12 m(4-2)(6) = 12\text{ m}, and Area 3 is 6+102(6−4)=16 m\frac{6+10}{2}(6-4) = 16\text{ m}, giving a total of 34 m34\text{ m}. Dividing by the total time of 6 s6\text{ s} yields an average velocity of 346≈5.67 m/s\frac{34}{6} \approx 5.67\text{ m/s}.

Question 4

Which one of the following statements is correct regarding the motion in a plane?

  1. A.When a body moves in a horizontal circle, its velocity is constant
  2. B.When a body moves in a vertical circle, its speed is constant
  3. C.The centripetal force for a body moving in either vertical or horizontal circle is toward the center
  4. D.In projectile motion the horizontal component of the motion is uniformly accelerated motion.
Show the answer and explanation

Answer: C The centripetal force for a body moving in either vertical or horizontal circle is toward the center

Why

By definition, the centripetal force is always directed toward the center of the circular trajectory for any circular motion. Option A is incorrect because the velocity vector continuously changes direction even if speed is constant.

Question 5

A bullet is fired at an angel of 30° above the horizontal. If air resistance is neglected, what should be the bullet's horizontal acceleration (ax⃗)(\vec{a_x}) and vertical acceleration (ay⃗)(\vec{a_y}) when it reaches its maximum height?

  1. A.Both ax⃗\vec{a_x} and ay⃗\vec{a_y} are zero
  2. B.ax⃗\vec{a_x} is 10 m/s2\mathrm{m/s^2} downward, and ay⃗\vec{a_y} is zero
  3. C.Both ax⃗\vec{a_x} and ay⃗\vec{a_y} are 10 m/s2\mathrm{m/s^2} downward
  4. D.ax⃗\vec{a_x} is zero, and ay⃗\vec{a_y} is 10 m/s2\mathrm{m/s^2} downward.
Show the answer and explanation

Answer: D ax⃗\vec{a_x} is zero, and ay⃗\vec{a_y} is 10 m/s2\mathrm{m/s^2} downward.

Why

In standard projectile motion neglecting air resistance, gravity acts solely downward with an acceleration of approximately 10 m/s210\text{ m/s}^2, while there is no force in the horizontal direction, so ax=0a_x = 0 throughout the flight.

Question 6

Two students A and B, with masses mAm_A and mBm_B respectively, stand on a wheeled trolleys as shown in the figure below. If student A has larger mass and pushes student B, then what can be said about their accelerations? [Figure: Line drawing of two boys facing each other, each standing on a small four-wheeled trolley (skateboard-like platform) resting on a hatched horizontal ground line. The boy on the left is labelled A, the boy on the right is labelled B. A leans forward with both arms extended, his hands pressing against B's hands, so A is pushing B to the right. Both boys are drawn about the same size; no forces or numerical values are marked.]

  1. A.The acceleration of student B is less than that of student A.
  2. B.Both boys will be accelerated by the same magnitude but in opposite directions.
  3. C.The acceleration of student A is less than that of student B.
  4. D.There would be no acceleration because the forcec are equal and opposite.
Show the answer and explanation

Answer: C The acceleration of student A is less than that of student B.

Why

According to Newton's third law, the forces exerted on both students are equal in magnitude and opposite in direction. Since acceleration is inversely proportional to mass (a=F/ma = F/m), the heavier student A experiences a smaller acceleration than student B.

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Physics papers from other years

2018 E.C. (2026)2017 E.C. (2025)2016 E.C. (2024)2015 E.C. (2023)2014 E.C. (2022)2013 E.C. (2021)2012 E.C. (2020)2011 E.C. (2019)2009 E.C. (2017)2008 E.C. (2016)2007 E.C. (2015)2006 E.C. (2014)2005 E.C. (2013)

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Are these the real 2010 E.C. Physics entrance exam questions?

Yes. They come from the national university entrance exam in Physics that students sat in 2010 E.C. (2018). Our set holds 41 of its questions, each with its answer and an explanation that points back to the textbook.

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