Ecuador · Grado 12 · Practice Sheet 11

1. 1.

   A 16 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   An object with initial velocity 9 m/s accelerates at 1.8 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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3. 3.

   Find the force needed to accelerate a 7 kg mass at 1.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A device runs at 76 V drawing 2.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the momentum of a 53 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the force needed to accelerate a 22 kg mass at 9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Two masses 5,400 kg and 350 kg are 18 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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8. 8.

   Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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9. 9.

   In a triangle, a = 14, b = 17 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A wave has frequency 897 Hz and wavelength 4.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A force of 418 N acts on an area of 7.9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A 32 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Two masses 5,000 kg and 620 kg are 2 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.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Find the force needed to accelerate a 4 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 314 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A force of 67 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A 30 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

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

    Formula:Quadratic Formula

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

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