Russia · Grade 12 · Practice Sheet 16

1. 1.

   Find the momentum of a 44 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A triangle has sides a = 15 cm and b = 14 cm with an included angle C = 90°. 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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3. 3.

   Two masses 4,600 kg and 400 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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4. 4.

   Find the force needed to accelerate a 11 kg mass at 4.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A triangle has sides a = 5 cm and b = 5 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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6. 6.

   Find the momentum of a 3 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   An object with initial velocity 0 m/s accelerates at 1 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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8. 8.

   A device runs at 84 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   ₽2,300 is invested at 3% compound interest per annum for 2 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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10. 10.

    A body starts at 0 m/s and accelerates at 3.3 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A wave has frequency 194 Hz and wavelength 3.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    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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13. 13.

    A force of 41 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A device runs at 61 V drawing 1.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    ₽2,000 is invested at 8% compound interest per annum for 2 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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16. 16.

    Find the force needed to accelerate a 2 kg mass at 1.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    An object with initial velocity 3 m/s accelerates at 2.9 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    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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19. 19.

    An object with initial velocity 6 m/s accelerates at 2.2 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the force needed to accelerate a 36 kg mass at 6.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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