Engineering Entrance · Practice Sheet 20

1. 1.

   Physics

   Find the electrical power when 118 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Physics

   Find the momentum of a 49 kg body moving at 15 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

   Formula:pH of a Solution

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

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4. 4.

   Mathematics

   Find the distance between the points (-7, -3) and (-8, -4).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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5. 5.

   Mathematics

   Evaluate log base 2 of 4.

   Formula:Logarithm Evaluation

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

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6. 6.

   Mathematics

   Evaluate ∫ from 0 to 4 of 2x^1 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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7. 7.

   Physics

   An object starts at 3 m/s and accelerates at 10 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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8. 8.

   Physics

   A constant force of 86 N moves an object 26 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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9. 9.

   Chemistry

   How many moles are present in 18 g of water (H₂O) (molar mass = 18 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Physics

    Find the voltage across a 45 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    Find the distance between the points (0, 7) and (2, 6).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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12. 12.

    Physics

    A projectile is launched at 50 m/s at 60° 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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13. 13.

    Chemistry

    39 mL of a 10 M solution is diluted to 166 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Physics

    Find the kinetic energy of a 13 kg object moving at 11 m/s.

    Formula:Kinetic Energy

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

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15. 15.

    Physics

    Calculate the potential energy of a 6 kg object at a height of 2 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Mathematics

    For the quadratic 4x² − 3x − 6 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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17. 17.

    Physics

    A force of 598 N acts on an area of 48 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Chemistry

    24 mL of a 5 M solution is diluted to 74 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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19. 19.

    Physics

    If 1,372 J of work is done in 40 s, find the power.

    Formula:Power

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

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20. 20.

    Chemistry

    Find the molarity of a solution containing 1.5 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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