AP Physics · Practice Sheet 13

1. 1.

   Mathematics

   Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   An object starts at 9 m/s and accelerates at 1 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Mathematics

   Find the distance between the points (-2, -6) and (3, 3).

   Formula:Distance Between Two Points

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

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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 1 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Physics

   Calculate the potential energy of a 42 kg object at a height of 36 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Mathematics

   Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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7. 7.

   Mathematics

   Find the distance between the points (-2, -3) and (1, -8).

   Formula:Distance Between Two Points

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

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8. 8.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 19 and common difference 3.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   Calculate the potential energy of a 29 kg object at a height of 32 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Physics

    Find the kinetic energy of a 6 kg object moving at 22 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Physics

    Calculate the potential energy of a 41 kg object at a height of 18 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Physics

    Find the force required to accelerate a 40 kg mass at 16 m/s².

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

    $F = ma$

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13. 13.

    Physics

    Find the electrical power when 127 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 9, find term number 18.

    Formula:AP nth Term

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

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15. 15.

    Physics

    Find the density of an object with mass 356 g and volume 17 cm³.

    Formula:Density

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

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16. 16.

    Physics

    A force of 506 N acts on an area of 18 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Mathematics

    If f(x) = 3x³ + 3x² + 9x, find f′(3).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Physics

    Calculate the potential energy of a 3 kg object at a height of 20 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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20. 20.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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