Cambodia · Grade 12 · Practice Sheet 50

1. 1.

   Find the momentum of a 49 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   In a triangle, a = 8, b = 6 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Two masses 8,300 kg and 810 kg are 8 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 12 m/s accelerates at 1.9 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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5. 5.

   A 16 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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7. 7.

   A wave has frequency 898 Hz and wavelength 1.08 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the sum of the first 5 terms of a geometric series with first term a = 3 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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9. 9.

   Find the gravitational potential energy of a 26 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 10 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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12. 12.

    Find the momentum of a 60 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the force needed to accelerate a 18 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    In a triangle, a = 10, b = 18 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A wave has frequency 569 Hz and wavelength 2.02 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A 39 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    In a triangle, a = 12, b = 8 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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18. 18.

    Find the force needed to accelerate a 58 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Two masses 4,500 kg and 810 kg are 6 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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20. 20.

    Find the momentum of a 19 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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