Ghana · Grade 12 · Practice Sheet 39

1. 1.

   Find the force needed to accelerate a 57 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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3. 3.

   A 4 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A population of 6,800 grows 2% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the population standard deviation of: 14, 11, 11, 2, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A force of 48 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A device runs at 48 V drawing 9.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Two masses 6,700 kg and 660 kg are 20 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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10. 10.

    A force of 41 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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11. 11.

    Find the gravitational potential energy of a 30 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the force needed to accelerate a 42 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A current of 5.8 A flows through a 53 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the force needed to accelerate a 17 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    An object with initial velocity 14 m/s accelerates at 2.1 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A device runs at 61 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A population of 3,200 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A device runs at 109 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 356 N acts on an area of 5.6 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A population of 7,300 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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