Poland · Klasa 12 · Practice Sheet 23

1. 1.

   A wave has frequency 154 Hz and wavelength 0.33 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the force needed to accelerate a 58 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A body starts at 10 m/s and accelerates at 3.4 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A cone has base radius 8 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the force needed to accelerate a 50 kg mass at 5.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the population standard deviation of: 15, 14, 7, 18, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   An object with initial velocity 7 m/s accelerates at 4.9 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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8. 8.

   Solve using the quadratic formula: x² − 2x − 3 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A wave has frequency 892 Hz and wavelength 0.93 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the population standard deviation of: 19, 13, 10, 8, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    An object with initial velocity 2 m/s accelerates at 3.5 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A force of 112 N acts on an area of 8.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A current of 7.9 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 24 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Two masses 4,100 kg and 680 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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16. 16.

    A cone has base radius 9 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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17. 17.

    Find the momentum of a 30 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 93 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A triangle has sides a = 7 cm and b = 5 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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20. 20.

    A current of 5.7 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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