AP Physics · Practice Sheet 28

1. 1.

   Physics

   Find the momentum of a 26 kg body moving at 17 m/s.

   Formula:Linear Momentum

   $p = mv$

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2. 2.

   Mathematics

   For the quadratic 4x² + 0x − 3 = 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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3. 3.

   Mathematics

   Find the sum of the first 6 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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4. 4.

   Physics

   Find the kinetic energy of a 11 kg object moving at 16 m/s.

   Formula:Kinetic Energy

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

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5. 5.

   Physics

   Find the voltage across a 2 Ω resistor carrying a current of 3 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   Physics

   Calculate the potential energy of a 34 kg object at a height of 34 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Mathematics

   Find the sum of the first 6 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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8. 8.

   Mathematics

   If f(x) = 5x³ + 4x² + 2x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Physics

   Find the force required to accelerate a 8 kg mass at 1 m/s².

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

   $F = ma$

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10. 10.

    Mathematics

    If f(x) = 1x³ + 3x² + 8x, find f′(4).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Physics

    A body moving at 8 m/s accelerates at 7 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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12. 12.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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13. 13.

    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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14. 14.

    Physics

    An object starts at 18 m/s and accelerates at 8 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Physics

    Find the momentum of a 45 kg body moving at 16 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Mathematics

    Find the slope of the line through (-6, 0) and (-5, 5).

    Formula:Slope of a Line

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

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17. 17.

    Mathematics

    Evaluate ∫ from 2 to 3 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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18. 18.

    Mathematics

    Find the distance between the points (-2, 1) and (-6, -2).

    Formula:Distance Between Two Points

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

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19. 19.

    Physics

    Find the force required to accelerate a 4 kg mass at 9 m/s².

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

    $F = ma$

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20. 20.

    Physics

    Find the voltage across a 34 Ω resistor carrying a current of 12 A.

    Formula:Ohm's Law

    $V = IR$

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