Russia · Grade 12 · Practice Sheet 28

1. 1.

   An object with initial velocity 4 m/s accelerates at 2.5 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   A current of 6 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Two masses 5,100 kg and 330 kg are 17 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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4. 4.

   Solve using the quadratic formula: x² + 1x − 30 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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5. 5.

   Find the momentum of a 33 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 37 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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7. 7.

   An object with initial velocity 14 m/s accelerates at 4 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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8. 8.

   Find the force needed to accelerate a 15 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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10. 10.

    A wave has frequency 839 Hz and wavelength 3.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A 27 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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13. 13.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    Find the population standard deviation of: 9, 17, 9, 20, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A force of 113 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A wave has frequency 195 Hz and wavelength 1.11 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A 11 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    A current of 6.1 A flows through a 57 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the force needed to accelerate a 36 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the population standard deviation of: 11, 13, 6, 4, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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