Austria · Klasse 10 · Practice Sheet 4

1. 1.

   Find the momentum of a 27 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A device runs at 179 V drawing 5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   An object with initial velocity 3 m/s accelerates at 1.6 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Find the gravitational potential energy of a 40 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   An object with initial velocity 7 m/s accelerates at 4.8 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A body starts at 1 m/s and accelerates at 2.1 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A cone has base radius 6 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   Solve using the quadratic formula: x² + 6x + 8 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A population of 8,200 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A wave has frequency 292 Hz and wavelength 3.2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the gravitational potential energy of a 45 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    €2,400 is invested at 6% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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14. 14.

    In a triangle, a = 17, b = 5 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    Find the force needed to accelerate a 46 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A body starts at 18 m/s and accelerates at 4.9 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A cone has base radius 9 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    €4,100 is invested at 5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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19. 19.

    Find the force needed to accelerate a 38 kg mass at 5.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    In a triangle, a = 13, b = 14 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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