Police & Armed Forces · Practice Sheet 14

1. 1.

   Physics

   Calculate the potential energy of a 11 kg object at a height of 30 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Physics

   A body moving at 10 m/s accelerates at 6 m/s² for 2 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

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

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3. 3.

   Physics

   Find the momentum of a 14 kg body moving at 13 m/s.

   Formula:Linear Momentum

   $p = mv$

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4. 4.

   Physics

   A body moving at 3 m/s accelerates at 5 m/s² for 6 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

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

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5. 5.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 7 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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7. 7.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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8. 8.

   Physics

   Find the force required to accelerate a 48 kg mass at 9 m/s².

   Formula:Newton's Second Law (F = ma)

   $F = ma$

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9. 9.

   Quantitative Aptitude

   The sum of the ages of two people is 47 years, and one is 13 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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10. 10.

    Quantitative Aptitude

    What is 50% of 380?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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11. 11.

    Physics

    Find the kinetic energy of a 3 kg object moving at 23 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

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12. 12.

    Physics

    Find the force required to accelerate a 20 kg mass at 6 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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13. 13.

    Physics

    A projectile is launched at 25 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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14. 14.

    Physics

    A body moving at 8 m/s accelerates at 1 m/s² for 6 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

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

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15. 15.

    Quantitative Aptitude

    Two varieties costing AED 22 and AED 74 per kg are mixed to give a mixture worth AED 45 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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16. 16.

    Quantitative Aptitude

    A vehicle covers 522 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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17. 17.

    Physics

    A force of 117 N acts on an area of 45 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    A constant force of 82 N moves an object 8 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Quantitative Aptitude

    A can finish a job in 19 days and B in 11 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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20. 20.

    Quantitative Aptitude

    The sum of the ages of two people is 51 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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