AP Physics · Practice Sheet 45

1. 1.

   Mathematics

   Find the distance between the points (-3, -4) and (-8, 6).

   Formula:Distance Between Two Points

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

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2. 2.

   Physics

   A constant force of 19 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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3. 3.

   Physics

   Find the kinetic energy of a 6 kg object moving at 11 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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5. 5.

   Physics

   Find the electrical power when 82 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Physics

   Find the momentum of a 4 kg body moving at 19 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Physics

   A body moving at 7 m/s accelerates at 4 m/s² for 8 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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8. 8.

   Physics

   Calculate the potential energy of a 22 kg object at a height of 6 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Mathematics

   If f(x) = 2x³ + 1x² + 3x, find f′(4).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Physics

    If 2,170 J of work is done in 35 s, find the power.

    Formula:Power

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

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11. 11.

    Physics

    Find the voltage across a 42 Ω resistor carrying a current of 1 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Mathematics

    Find the slope of the line through (1, -5) and (-1, 4).

    Formula:Slope of a Line

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

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13. 13.

    Physics

    Find the density of an object with mass 430 g and volume 5 cm³.

    Formula:Density

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

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14. 14.

    Mathematics

    Find the distance between the points (-8, 3) and (7, 8).

    Formula:Distance Between Two Points

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

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15. 15.

    Physics

    Find the force required to accelerate a 24 kg mass at 8 m/s².

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

    $F = ma$

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16. 16.

    Physics

    An object starts at 1 m/s and accelerates at 7 m/s² for 2 s. Find its final velocity.

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

    $v = u + at$

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17. 17.

    Mathematics

    Evaluate ∫ from 1 to 5 of 4x^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.

    Physics

    Find the voltage across a 31 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Mathematics

    For the quadratic 1x² − 6x − 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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20. 20.

    Mathematics

    Find term number 6 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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