AP Physics · Practice Sheet 3

1. 1.

   Physics

   Find the density of an object with mass 289 g and volume 49 cm³.

   Formula:Density

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

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2. 2.

   Physics

   A constant force of 124 N moves an object 47 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Physics

   Find the kinetic energy of a 16 kg object moving at 17 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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5. 5.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 4 and common difference 6.

   Formula:AP Sum of n Terms

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

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6. 6.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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7. 7.

   Mathematics

   For the quadratic 4x² − 8x − 7 = 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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8. 8.

   Physics

   If 349 J of work is done in 4 s, find the power.

   Formula:Power

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

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9. 9.

   Physics

   A projectile is launched at 16 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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10. 10.

    Mathematics

    Find the slope of the line through (-6, 1) and (6, 7).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    Evaluate ∫ from 0 to 5 of 4x^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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12. 12.

    Physics

    Find the force required to accelerate a 20 kg mass at 16 m/s².

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

    $F = ma$

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13. 13.

    Mathematics

    Evaluate ∫ from 1 to 4 of 2x^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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14. 14.

    Physics

    Find the electrical power when 43 V drives a current of 19 A.

    Formula:Electrical Power

    $P = VI$

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15. 15.

    Physics

    Find the kinetic energy of a 8 kg object moving at 18 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Physics

    If 983 J of work is done in 19 s, find the power.

    Formula:Power

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

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17. 17.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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18. 18.

    Physics

    Calculate the potential energy of a 23 kg object at a height of 48 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Physics

    If 4,641 J of work is done in 32 s, find the power.

    Formula:Power

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

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20. 20.

    Mathematics

    Find the distance between the points (5, -2) and (5, -4).

    Formula:Distance Between Two Points

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

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