Spain · Grado 10 · Practice Sheet 47

1. 1.

   A body starts at 13 m/s and accelerates at 1.7 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Find the momentum of a 53 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A wave has frequency 836 Hz and wavelength 4.94 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the gravitational potential energy of a 12 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A wave has frequency 60 Hz and wavelength 3.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the gravitational potential energy of a 4 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A body starts at 0 m/s and accelerates at 3 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the force needed to accelerate a 3 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the gravitational potential energy of a 8 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the force needed to accelerate a 29 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A wave has frequency 748 Hz and wavelength 3.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A right-angled triangle has legs of 5 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A population of 3,200 grows 8% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A force of 249 N acts on an area of 4.1 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the gravitational potential energy of a 15 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    €3,500 is invested at 5% 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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18. 18.

    Solve for x: 3x + 2 = 17.

    Formula:Solving a Linear Equation

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

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19. 19.

    A right-angled triangle has legs of 5 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A value changes from 97 to 247. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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