EmSAT Achieve · Practice Sheet 37

1. 1.

   Physics

   If 536 J of work is done in 23 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Find the voltage across a 19 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Physics

   A body moving at 5 m/s accelerates at 8 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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4. 4.

   Physics

   Find the momentum of a 13 kg body moving at 22 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Mathematics

   Find the distance between the points (-2, -4) and (4, 5).

   Formula:Distance Between Two Points

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

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6. 6.

   Physics

   Find the voltage across a 4 Ω resistor carrying a current of 9 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Chemistry

   26 mL of a 5 M solution is diluted to 142 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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8. 8.

   Physics

   Find the density of an object with mass 129 g and volume 9 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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9. 9.

   Biology

   Calculate the BMI of a person weighing 56 kg with height 1.6 m.

   Formula:Body Mass Index

   $BMI = \dfrac{m}{h^{2}}$

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10. 10.

    Physics

    An object starts at 2 m/s and accelerates at 5 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    Find the kinetic energy of a 9 kg object moving at 25 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Physics

    If 1,235 J of work is done in 48 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    Find the electrical power when 199 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 280 K in a 12 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 3 of 5x^3 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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16. 16.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Physics

    A body moving at 0 m/s accelerates at 3 m/s² for 9 s. Find the distance travelled.

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

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

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18. 18.

    Physics

    Find the force required to accelerate a 15 kg mass at 15 m/s².

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

    $F = ma$

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19. 19.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 2 and common difference 2.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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