South Africa · Grade 12 · Practice Sheet 33

1. 1.

   A 30 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A wave has frequency 743 Hz and wavelength 2.06 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the population standard deviation of: 4, 14, 19, 19, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A population of 8,800 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   R2,400 is invested at 5% compound interest per annum for 4 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.

   An object with initial velocity 6 m/s accelerates at 3.5 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A force of 246 N acts on an area of 9.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the population standard deviation of: 2, 13, 12, 15, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A cone has base radius 8 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A 33 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    An object with initial velocity 14 m/s accelerates at 2.4 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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12. 12.

    Find the force needed to accelerate a 23 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the momentum of a 37 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Two masses 6,800 kg and 270 kg are 13 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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15. 15.

    A 21 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the force needed to accelerate a 54 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cone has base radius 6 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A device runs at 9 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A 17 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Find the momentum of a 50 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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