AP Physics · Practice Sheet 17

1. 1.

   Physics

   Find the kinetic energy of a 18 kg object moving at 29 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Mathematics

   Find term number 3 of a geometric progression with first term 3 and common ratio 3.

   Formula:GP nth Term

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

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3. 3.

   Mathematics

   Evaluate ∫ from 2 to 5 of 2x^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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4. 4.

   Physics

   If 3,117 J of work is done in 3 s, find the power.

   Formula:Power

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

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5. 5.

   Mathematics

   For the quadratic 3x² + 6x − 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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6. 6.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 3, find term number 12.

   Formula:AP nth Term

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

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7. 7.

   Mathematics

   Find the distance between the points (1, -4) and (-7, 7).

   Formula:Distance Between Two Points

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

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8. 8.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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10. 10.

    Physics

    Find the electrical power when 112 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Physics

    Find the density of an object with mass 321 g and volume 22 cm³.

    Formula:Density

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

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12. 12.

    Mathematics

    If f(x) = 1x³ + 5x² + 2x, find f′(1).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Physics

    A projectile is launched at 44 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

    Find the voltage across a 50 Ω resistor carrying a current of 16 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Physics

    An object starts at 9 m/s and accelerates at 4 m/s² for 2 s. Find its final velocity.

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

    $v = u + at$

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16. 16.

    Mathematics

    Find the distance between the points (8, -5) and (3, 1).

    Formula:Distance Between Two Points

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

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17. 17.

    Physics

    Find the density of an object with mass 443 g and volume 28 cm³.

    Formula:Density

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

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18. 18.

    Mathematics

    For the quadratic 2x² + 7x + 4 = 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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19. 19.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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20. 20.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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