AP Physics · Practice Sheet 44

1. 1.

   Mathematics

   Evaluate ∫ from 0 to 3 of 5x^2 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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2. 2.

   Physics

   A constant force of 128 N moves an object 32 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Physics

   A body moving at 8 m/s accelerates at 6 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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4. 4.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 6 and common difference 2.

   Formula:AP Sum of n Terms

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

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5. 5.

   Physics

   Find the density of an object with mass 218 g and volume 42 cm³.

   Formula:Density

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

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6. 6.

   Physics

   Find the force required to accelerate a 3 kg mass at 16 m/s².

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

   $F = ma$

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7. 7.

   Physics

   An object starts at 11 m/s and accelerates at 9 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

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8. 8.

   Mathematics

   For the quadratic 3x² + 7x − 2 = 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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9. 9.

   Physics

   A projectile is launched at 39 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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10. 10.

    Mathematics

    Evaluate ∫ from 1 to 4 of 5x^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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11. 11.

    Physics

    An object starts at 0 m/s and accelerates at 7 m/s² for 4 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Physics

    Find the density of an object with mass 242 g and volume 37 cm³.

    Formula:Density

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

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13. 13.

    Physics

    A force of 575 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Physics

    A body moving at 10 m/s accelerates at 5 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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15. 15.

    Physics

    A constant force of 166 N moves an object 31 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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16. 16.

    Physics

    If 4,653 J of work is done in 16 s, find the power.

    Formula:Power

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

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17. 17.

    Mathematics

    Evaluate ∫ from 0 to 4 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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18. 18.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 7, find term number 15.

    Formula:AP nth Term

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

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20. 20.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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