AP Physics · Practice Sheet 42

1. 1.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 4 and common ratio 2.

   Formula:GP Sum of n Terms

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

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2. 2.

   Physics

   If 2,161 J of work is done in 46 s, find the power.

   Formula:Power

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

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3. 3.

   Physics

   Calculate the potential energy of a 21 kg object at a height of 38 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Physics

   Find the kinetic energy of a 1 kg object moving at 28 m/s.

   Formula:Kinetic Energy

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

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5. 5.

   Physics

   If 1,009 J of work is done in 18 s, find the power.

   Formula:Power

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

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6. 6.

   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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7. 7.

   Mathematics

   If f(x) = 4x³ + 3x² + 7x, find f′(4).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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8. 8.

   Physics

   Calculate the potential energy of a 23 kg object at a height of 17 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Physics

   Find the density of an object with mass 40 g and volume 4 cm³.

   Formula:Density

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

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10. 10.

    Mathematics

    Find the distance between the points (-5, -3) and (-4, -1).

    Formula:Distance Between Two Points

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

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11. 11.

    Physics

    A force of 907 N acts on an area of 10 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    A body moving at 13 m/s accelerates at 3 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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13. 13.

    Physics

    Calculate the potential energy of a 8 kg object at a height of 23 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Physics

    Find the density of an object with mass 349 g and volume 49 cm³.

    Formula:Density

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

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15. 15.

    Physics

    A body moving at 8 m/s accelerates at 4 m/s² for 5 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 force of 273 N acts on an area of 25 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Physics

    Find the force required to accelerate a 39 kg mass at 19 m/s².

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

    $F = ma$

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18. 18.

    Physics

    A constant force of 127 N moves an object 28 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

    If f(x) = 1x³ + 5x² + 1x, find f′(3).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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20. 20.

    Physics

    Find the kinetic energy of a 18 kg object moving at 19 m/s.

    Formula:Kinetic Energy

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

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