France · Classe 12 · Practice Sheet 40

1. 1.

   Find the momentum of a 59 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Two masses 2,100 kg and 860 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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3. 3.

   €1,300 is invested at 5% compound interest per annum for 3 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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4. 4.

   A current of 7.2 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A cone has base radius 3 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A device runs at 12 V drawing 1.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   An object with initial velocity 12 m/s accelerates at 3.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A current of 5.9 A flows through a 16 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A force of 33 N acts on an area of 2 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 455 Hz and wavelength 4.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A current of 7.6 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A force of 477 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A population of 5,400 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    Solve using the quadratic formula: x² + 1x − 12 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A force of 185 N acts on an area of 6.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

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

    Formula:Quadratic Formula

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

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17. 17.

    A device runs at 105 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    In a triangle, a = 10, b = 11 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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19. 19.

    A wave has frequency 611 Hz and wavelength 1.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the force needed to accelerate a 18 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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