Austria · Klasse 12 · Practice Sheet 50

1. 1.

   A 30 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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2. 2.

   Find the momentum of a 11 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A body starts at 15 m/s and accelerates at 4.8 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the gravitational potential energy of a 27 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the population standard deviation of: 5, 12, 8, 5, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   A wave has frequency 895 Hz and wavelength 3.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A population of 5,000 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   An object with initial velocity 5 m/s accelerates at 1.8 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the population standard deviation of: 9, 20, 11, 7, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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10. 10.

    Find the force needed to accelerate a 48 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the gravitational potential energy of a 15 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A cone has base radius 7 cm and height 17 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.

    A force of 8 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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14. 14.

    A cone has base radius 12 cm and height 5 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.

    Find the force needed to accelerate a 32 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A body starts at 7 m/s and accelerates at 2.2 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    Find the momentum of a 15 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the gravitational potential energy of a 23 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    In a triangle, a = 17, b = 17 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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