South Korea · Grade 12 · Practice Sheet 33

1. 1.

   An object with initial velocity 9 m/s accelerates at 2.1 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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2. 2.

   A force of 75 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A body starts at 8 m/s and accelerates at 4.6 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A triangle has sides a = 18 cm and b = 16 cm with an included angle C = 45°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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5. 5.

   A force of 96 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the gravitational potential energy of a 21 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A cone has base radius 7 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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9. 9.

   A cone has base radius 8 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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10. 10.

    Find the momentum of a 40 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the population standard deviation of: 5, 16, 12, 16, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    Find the gravitational potential energy of a 34 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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14. 14.

    Find the force needed to accelerate a 15 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 44 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the force needed to accelerate a 42 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A current of 0.9 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the gravitational potential energy of a 48 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the momentum of a 39 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Two masses 6,800 kg and 240 kg are 16 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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