Netherlands · Year 12 · Practice Sheet 3

1. 1.

   Find the force needed to accelerate a 35 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A force of 120 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the momentum of a 27 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A cone has base radius 4 cm and height 21 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 46 V drawing 1.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A triangle has sides a = 12 cm and b = 17 cm with an included angle C = 60°. 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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8. 8.

   A 40 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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9. 9.

   €1,000 is invested at 8% compound interest per annum for 5 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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10. 10.

    Find the gravitational potential energy of a 36 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the population standard deviation of: 15, 7, 17, 19, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    A device runs at 211 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A population of 7,000 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    €3,400 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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15. 15.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A force of 15 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Two masses 8,200 kg and 140 kg are 4 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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18. 18.

    A 14 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A device runs at 217 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the gravitational potential energy of a 14 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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