A-Level Physics · Practice Sheet 47

1. 1.

   Physics

   A body moving at 2 m/s accelerates at 8 m/s² for 10 s. Find the distance travelled.

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

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

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2. 2.

   Mathematics

   Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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3. 3.

   Physics

   Find the kinetic energy of a 16 kg object moving at 25 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Physics

   A force of 637 N acts on an area of 29 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Mathematics

   Find the slope of the line through (-2, 7) and (-3, -6).

   Formula:Slope of a Line

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

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6. 6.

   Physics

   Find the electrical power when 236 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   Find the momentum of a 20 kg body moving at 8 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 20 and common difference 9.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   An object starts at 1 m/s and accelerates at 4 m/s² for 10 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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11. 11.

    Physics

    If 1,163 J of work is done in 28 s, find the power.

    Formula:Power

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

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12. 12.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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13. 13.

    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    Find the density of an object with mass 91 g and volume 46 cm³.

    Formula:Density

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

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15. 15.

    Physics

    A body moving at 13 m/s accelerates at 1 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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16. 16.

    Physics

    A constant force of 85 N moves an object 12 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Mathematics

    Find the slope of the line through (-6, 2) and (7, 3).

    Formula:Slope of a Line

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

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18. 18.

    Physics

    A force of 177 N acts on an area of 38 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Mathematics

    For the quadratic 1x² − 2x + 0 = 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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20. 20.

    Physics

    Find the force required to accelerate a 23 kg mass at 18 m/s².

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

    $F = ma$

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