Sweden · Grade 11 · Practice Sheet 10

1. 1.

   Find the gravitational potential energy of a 45 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   An object with initial velocity 13 m/s accelerates at 2.9 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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3. 3.

   Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A right-angled triangle has legs of 4 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the momentum of a 17 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the force needed to accelerate a 54 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the momentum of a 57 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A triangle has sides a = 19 cm and b = 12 cm with an included angle C = 45°. 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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9. 9.

   A current of 6.7 A flows through a 38 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A 4 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Find the force needed to accelerate a 38 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the momentum of a 54 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    An object with initial velocity 3 m/s accelerates at 2.5 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A population of 1,900 grows 2% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A cone has base radius 3 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A body starts at 19 m/s and accelerates at 2.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 3 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A force of 426 N acts on an area of 8.5 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    A body starts at 0 m/s and accelerates at 5.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A cone has base radius 8 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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