Belgium · Year 12 · Practice Sheet 31

1. 1.

   A 29 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A force of 176 N acts on an area of 6.6 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the momentum of a 9 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the force needed to accelerate a 22 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A 24 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A triangle has sides a = 18 cm and b = 10 cm with an included angle C = 30°. 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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7. 7.

   A wave has frequency 378 Hz and wavelength 3.57 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the gravitational potential energy of a 3 kg object raised 23 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

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

   Formula:Sum of a Geometric Series

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

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10. 10.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the force needed to accelerate a 16 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Two masses 8,100 kg and 830 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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13. 13.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 8 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the momentum of a 5 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the force needed to accelerate a 24 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the momentum of a 14 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 10 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    €1,900 is invested at 3% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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19. 19.

    A current of 2.8 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A body starts at 11 m/s and accelerates at 5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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