AP Physics · Practice Sheet 49

1. 1.

   Physics

   If 2,563 J of work is done in 14 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Find the voltage across a 39 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Physics

   Calculate the potential energy of a 48 kg object at a height of 28 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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5. 5.

   Physics

   Find the kinetic energy of a 12 kg object moving at 3 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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7. 7.

   Physics

   A projectile is launched at 49 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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8. 8.

   Physics

   Find the kinetic energy of a 13 kg object moving at 23 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Mathematics

   Find the sum of the first 18 terms of an AP with first term 3 and common difference 3.

   Formula:AP Sum of n Terms

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

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10. 10.

    Physics

    Find the density of an object with mass 459 g and volume 48 cm³.

    Formula:Density

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

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11. 11.

    Physics

    If 2,231 J of work is done in 16 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    A force of 518 N acts on an area of 14 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    Physics

    Find the electrical power when 30 V drives a current of 15 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Mathematics

    Find the slope of the line through (8, 5) and (5, -8).

    Formula:Slope of a Line

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

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15. 15.

    Mathematics

    In an arithmetic progression with first term 7 and common difference 9, find term number 14.

    Formula:AP nth Term

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

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16. 16.

    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 16 and common difference 10, find term number 19.

    Formula:AP nth Term

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

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18. 18.

    Physics

    An object starts at 12 m/s and accelerates at 2 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Mathematics

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

    Formula:Distance Between Two Points

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

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20. 20.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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