India · Class 12 · Practice Sheet 6

1. 1.

   A body starts at 19 m/s and accelerates at 2.3 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A force of 30 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A population of 7,800 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A body starts at 1 m/s and accelerates at 2.3 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Find the sum of the first 6 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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6. 6.

   A triangle has sides a = 7 cm and b = 20 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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7. 7.

   Find the momentum of a 51 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the population standard deviation of: 18, 2, 18, 8, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the gravitational potential energy of a 8 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 70 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    ₹1,200 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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13. 13.

    A force of 373 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the force needed to accelerate a 22 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the momentum of a 34 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Two masses 8,600 kg and 200 kg are 17 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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17. 17.

    Find the momentum of a 49 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A body starts at 18 m/s and accelerates at 4.9 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A wave has frequency 865 Hz and wavelength 2.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A body starts at 4 m/s and accelerates at 3.9 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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