Ecuador · Grado 12 · Practice Sheet 34

1. 1.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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2. 2.

   Two masses 7,800 kg and 200 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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3. 3.

   Find the force needed to accelerate a 17 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 86 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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5. 5.

   A 31 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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6. 6.

   A force of 105 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A body starts at 1 m/s and accelerates at 3.2 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the force needed to accelerate a 48 kg mass at 2.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the gravitational potential energy of a 50 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Solve using the quadratic formula: x² − 2x − 8 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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11. 11.

    A body starts at 11 m/s and accelerates at 4.1 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the momentum of a 39 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A wave has frequency 91 Hz and wavelength 1.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the momentum of a 14 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the force needed to accelerate a 37 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 11 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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17. 17.

    A body starts at 14 m/s and accelerates at 3.9 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the momentum of a 46 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A wave has frequency 81 Hz and wavelength 1.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A force of 36 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

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

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