Italy · Classe 11 · Practice Sheet 36

1. 1.

   Find the force needed to accelerate a 2 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Solve using the quadratic formula: x² − 6x + 8 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Two masses 1,800 kg and 420 kg are 11 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.

   An object with initial velocity 9 m/s accelerates at 3.3 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A triangle has sides a = 20 cm and b = 15 cm with an included angle C = 90°. 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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6. 6.

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

   Formula:Volume of a Cone

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

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7. 7.

   In a triangle, a = 10, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   Two masses 4,900 kg and 820 kg are 20 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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9. 9.

   A wave has frequency 233 Hz and wavelength 1.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the momentum of a 52 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    An object with initial velocity 9 m/s accelerates at 1.8 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Solve using the quadratic formula: x² − 3x − 18 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A population of 4,100 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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14. 14.

    A 29 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the gravitational potential energy of a 30 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the force needed to accelerate a 14 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Two masses 1,400 kg and 130 kg are 3 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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18. 18.

    A cylinder has radius 3 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A wave has frequency 584 Hz and wavelength 0.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Two masses 6,600 kg and 830 kg are 14 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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