Austria · Klasse 11 · Practice Sheet 4

1. 1.

   Find the force needed to accelerate a 43 kg mass at 2.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A current of 5.4 A flows through a 49 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A body starts at 4 m/s and accelerates at 3.2 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Two masses 6,800 kg and 320 kg are 11 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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5. 5.

   A right-angled triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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6. 6.

   €2,200 is invested at 4% 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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7. 7.

   A population of 1,400 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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8. 8.

   A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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9. 9.

   A 10 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    An object with initial velocity 15 m/s accelerates at 4.5 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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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the momentum of a 40 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    In a triangle, a = 18, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A wave has frequency 712 Hz and wavelength 4.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 15 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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16. 16.

    An object with initial velocity 7 m/s accelerates at 4.5 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A force of 27 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A current of 5.2 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the momentum of a 21 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A device runs at 198 V drawing 9.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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