New Zealand · Year 12 · Practice Sheet 28

1. 1.

   An object with initial velocity 1 m/s accelerates at 4.8 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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2. 2.

   A force of 301 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the momentum of a 53 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A wave has frequency 494 Hz and wavelength 3.94 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the momentum of a 56 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A wave has frequency 657 Hz and wavelength 4.84 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   In a triangle, a = 12, b = 7 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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9. 9.

   A force of 170 N acts on an area of 4.9 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the momentum of a 28 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A cone has base radius 5 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A device runs at 130 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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16. 16.

    An object with initial velocity 2 m/s accelerates at 1.2 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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17. 17.

    A 7 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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18. 18.

    A force of 52 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the gravitational potential energy of a 30 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the population standard deviation of: 3, 3, 9, 13, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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