Engineering Entrance · Practice Sheet 23

1. 1.

   Physics

   Find the kinetic energy of a 14 kg object moving at 2 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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3. 3.

   Physics

   Find the kinetic energy of a 14 kg object moving at 13 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Mathematics

   Find the slope of the line through (-4, 7) and (4, -4).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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5. 5.

   Chemistry

   How many moles are present in 44 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

   $n = \dfrac{m}{M}$

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6. 6.

   Chemistry

   62 mL of a 2 M solution is diluted to 149 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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7. 7.

   Physics

   Calculate the potential energy of a 40 kg object at a height of 4 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Physics

   Find the kinetic energy of a 16 kg object moving at 18 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 6, find term number 22.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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10. 10.

    Physics

    If 4,909 J of work is done in 4 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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11. 11.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻4 mol/L.

    Formula:pH of a Solution

    $pH = -\log_{10}[H^{+}]$

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12. 12.

    Physics

    Find the kinetic energy of a 14 kg object moving at 25 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Physics

    A projectile is launched at 43 m/s at 30° 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

    If 4,651 J of work is done in 13 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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15. 15.

    Physics

    Find the voltage across a 31 Ω resistor carrying a current of 16 A.

    Formula:Ohm's Law

    $V = IR$

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16. 16.

    Mathematics

    Find term number 6 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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17. 17.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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18. 18.

    Physics

    An object starts at 11 m/s and accelerates at 9 m/s² for 12 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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19. 19.

    Physics

    A body moving at 5 m/s accelerates at 3 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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20. 20.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 1 L of solution.

    Formula:Molarity

    $M = \dfrac{n}{V}$

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