Canada · Grade 12 · Practice Sheet 39

1. 1.

   A 37 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Find the force needed to accelerate a 41 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A body starts at 19 m/s and accelerates at 5 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the force needed to accelerate a 24 kg mass at 2.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A force of 12 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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6. 6.

   Find the gravitational potential energy of a 3 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   $3,500 is invested at 6% 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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8. 8.

   Two masses 3,200 kg and 860 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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9. 9.

   Find the force needed to accelerate a 56 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the gravitational potential energy of a 17 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 44 V drawing 5.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A cone has base radius 6 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    Find the momentum of a 5 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A cone has base radius 9 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Solve using the quadratic formula: x² + 10x + 24 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A device runs at 80 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 11 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A body starts at 18 m/s and accelerates at 1.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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