AP Physics · Practice Sheet 5

1. 1.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 5 and common ratio 3.

   Formula:GP Sum of n Terms

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

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2. 2.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 1 and common difference 8.

   Formula:AP Sum of n Terms

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

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3. 3.

   Physics

   If 4,456 J of work is done in 40 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

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5. 5.

   Physics

   Find the kinetic energy of a 12 kg object moving at 4 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 3 and common ratio 3.

   Formula:GP Sum of n Terms

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

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7. 7.

   Mathematics

   If f(x) = 3x³ + 4x² + 8x, find f′(4).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Find the sum of the first 6 terms of an AP with first term 18 and common difference 6.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   Find the momentum of a 17 kg body moving at 11 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    Find the force required to accelerate a 45 kg mass at 7 m/s².

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

    $F = ma$

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11. 11.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    Find the momentum of a 30 kg body moving at 25 m/s.

    Formula:Linear Momentum

    $p = mv$

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13. 13.

    Physics

    A projectile is launched at 26 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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14. 14.

    Physics

    A force of 742 N acts on an area of 36 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Mathematics

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

    Formula:Slope of a Line

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

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16. 16.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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17. 17.

    Mathematics

    Find the distance between the points (-4, -4) and (-7, -2).

    Formula:Distance Between Two Points

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

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18. 18.

    Physics

    If 3,798 J of work is done in 40 s, find the power.

    Formula:Power

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 7 and common difference 6, find term number 26.

    Formula:AP nth Term

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

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20. 20.

    Physics

    Find the electrical power when 116 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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