Austria · Klasse 10 · Practice Sheet 46

1. 1.

   An object with initial velocity 1 m/s accelerates at 3.5 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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2. 2.

   Find the force needed to accelerate a 23 kg mass at 2.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 81 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Solve for x: 5x + 12 = 32.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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5. 5.

   An object with initial velocity 5 m/s accelerates at 1.5 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A cylinder has radius 7 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   In a triangle, a = 17, b = 11 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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8. 8.

   A 5 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A current of 3.7 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A bag has 13 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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11. 11.

    A body starts at 9 m/s and accelerates at 4.8 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    €1,900 is invested at 3% compound interest per annum for 4 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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13. 13.

    €2,200 is invested at 4% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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14. 14.

    A device runs at 96 V drawing 2.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the momentum of a 29 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A cone has base radius 3 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A right-angled triangle has legs of 16 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the force needed to accelerate a 13 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A right-angled triangle has legs of 18 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A force of 184 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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