Bahrain · Grade 12 · Practice Sheet 23

1. 1.

   Find the force needed to accelerate a 43 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   In a triangle, a = 15, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Find the population standard deviation of: 2, 7, 4, 13, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the gravitational potential energy of a 37 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the population standard deviation of: 18, 17, 7, 4, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the gravitational potential energy of a 41 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   An object with initial velocity 13 m/s accelerates at 1.1 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   BD 2,000 is invested at 8% 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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9. 9.

   Find the force needed to accelerate a 16 kg mass at 4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Two masses 1,200 kg and 250 kg are 5 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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11. 11.

    A force of 91 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A 15 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A force of 85 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    An object with initial velocity 3 m/s accelerates at 2.8 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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15. 15.

    A wave has frequency 816 Hz and wavelength 1.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A cone has base radius 9 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the momentum of a 26 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 72 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A body starts at 8 m/s and accelerates at 3.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the momentum of a 12 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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