Pakistan · Class 12 · Practice Sheet 10

1. 1.

   A 36 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A wave has frequency 452 Hz and wavelength 3.8 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A body starts at 4 m/s and accelerates at 4.6 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the force needed to accelerate a 34 kg mass at 2.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A body starts at 19 m/s and accelerates at 2.9 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the population standard deviation of: 9, 14, 10, 12, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A force of 57 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A wave has frequency 273 Hz and wavelength 2.17 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A body starts at 19 m/s and accelerates at 1.4 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 7 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    In a triangle, a = 6, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    ₨2,200 is invested at 8% compound interest per annum for 5 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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14. 14.

    A force of 458 N acts on an area of 2.5 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    In a triangle, a = 16, b = 6 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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16. 16.

    A force of 471 N acts on an area of 2.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 31 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A 25 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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19. 19.

    An object with initial velocity 9 m/s accelerates at 3.3 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the gravitational potential energy of a 2 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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