United Kingdom · Year 12 · Practice Sheet 33

1. 1.

   A wave has frequency 685 Hz and wavelength 0.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   An object with initial velocity 13 m/s accelerates at 4.6 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A force of 86 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the momentum of a 2 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A body starts at 10 m/s and accelerates at 2.3 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Find the gravitational potential energy of a 20 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A force of 295 N acts on an area of 1.9 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A triangle has sides a = 16 cm and b = 9 cm with an included angle C = 30°. 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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10. 10.

    Find the momentum of a 8 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A 27 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 7 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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13. 13.

    A cone has base radius 11 cm and height 22 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.

    A force of 8 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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15. 15.

    A body starts at 13 m/s and accelerates at 2.8 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the gravitational potential energy of a 13 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A triangle has sides a = 18 cm and b = 8 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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18. 18.

    In a triangle, a = 9, b = 13 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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19. 19.

    A wave has frequency 720 Hz and wavelength 0.85 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the momentum of a 38 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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