AP Physics · Practice Sheet 2

1. 1.

   Physics

   Find the density of an object with mass 500 g and volume 45 cm³.

   Formula:Density

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

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2. 2.

   Physics

   Find the kinetic energy of a 6 kg object moving at 27 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   An object starts at 14 m/s and accelerates at 8 m/s² for 11 s. Find its final velocity.

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

   $v = u + at$

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4. 4.

   Physics

   If 114 J of work is done in 31 s, find the power.

   Formula:Power

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

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5. 5.

   Physics

   Find the kinetic energy of a 1 kg object moving at 12 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Physics

   Calculate the potential energy of a 21 kg object at a height of 27 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Physics

   Find the momentum of a 27 kg body moving at 6 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Physics

   A projectile is launched at 37 m/s at 30° 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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9. 9.

   Physics

   Find the density of an object with mass 309 g and volume 17 cm³.

   Formula:Density

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

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10. 10.

    Mathematics

    Find the distance between the points (-2, -1) and (-7, 5).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    If f(x) = 4x³ + 3x² + 4x, find f′(1).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Mathematics

    Evaluate ∫ from 1 to 4 of 1x^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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14. 14.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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15. 15.

    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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16. 16.

    Mathematics

    For the quadratic 5x² − 8x + 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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17. 17.

    Physics

    Find the force required to accelerate a 26 kg mass at 2 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

    Find the sum of the first 6 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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19. 19.

    Physics

    Calculate the potential energy of a 5 kg object at a height of 40 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 11 and common difference 10.

    Formula:AP Sum of n Terms

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

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