New Zealand · Year 12 · Practice Sheet 13

1. 1.

   A device runs at 196 V drawing 7.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   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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3. 3.

   Find the gravitational potential energy of a 17 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the momentum of a 54 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A body starts at 9 m/s and accelerates at 2.4 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A current of 5.1 A flows through a 50 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A device runs at 176 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A current of 2.5 A flows through a 45 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A population of 4,000 grows 8% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

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

    Formula:Quadratic Formula

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

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11. 11.

    A force of 89 N acts on an area of 5.5 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Find the momentum of a 12 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A cone has base radius 4 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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14. 14.

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

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the gravitational potential energy of a 20 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A population of 6,500 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A 19 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A wave has frequency 188 Hz and wavelength 4.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the gravitational potential energy of a 3 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A device runs at 185 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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