Finland · Grade 12 · Practice Sheet 34

1. 1.

   Two masses 4,300 kg and 460 kg are 10 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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2. 2.

   A body starts at 20 m/s and accelerates at 1.5 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A force of 382 N acts on an area of 9.7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

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

   Formula:Quadratic Formula

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

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5. 5.

   €4,000 is invested at 3% compound interest per annum for 2 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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6. 6.

   A current of 1.1 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A 6 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A force of 490 N acts on an area of 0.8 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the gravitational potential energy of a 10 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A population of 7,200 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Find the momentum of a 8 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A triangle has sides a = 5 cm and b = 16 cm with an included angle C = 120°. 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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13. 13.

    Solve using the quadratic formula: x² − 3x − 4 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A wave has frequency 716 Hz and wavelength 3.98 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A device runs at 19 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 4 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    A force of 16 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the force needed to accelerate a 4 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A device runs at 115 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 44 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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