AP Physics · Practice Sheet 37

1. 1.

   Physics

   A projectile is launched at 43 m/s at 45° 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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2. 2.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 6 and common ratio 3.

   Formula:GP Sum of n Terms

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

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3. 3.

   Physics

   A constant force of 71 N moves an object 28 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Physics

   Find the density of an object with mass 282 g and volume 48 cm³.

   Formula:Density

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

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5. 5.

   Mathematics

   If f(x) = 5x³ + 3x² + 4x, find f′(4).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Physics

   Find the kinetic energy of a 10 kg object moving at 22 m/s.

   Formula:Kinetic Energy

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

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7. 7.

   Physics

   Calculate the potential energy of a 2 kg object at a height of 7 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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9. 9.

   Mathematics

   If f(x) = 1x³ + 5x² + 2x, find f′(4).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Mathematics

    Find the slope of the line through (-8, -8) and (8, -1).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    Find the kinetic energy of a 10 kg object moving at 21 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 9, find term number 11.

    Formula:AP nth Term

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

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13. 13.

    Physics

    Find the electrical power when 17 V drives a current of 7 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Mathematics

    Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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15. 15.

    Physics

    An object starts at 17 m/s and accelerates at 10 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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16. 16.

    Physics

    A constant force of 78 N moves an object 35 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Mathematics

    Find the slope of the line through (4, 4) and (8, 4).

    Formula:Slope of a Line

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

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18. 18.

    Physics

    A body moving at 9 m/s accelerates at 7 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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19. 19.

    Physics

    Find the force required to accelerate a 43 kg mass at 16 m/s².

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

    $F = ma$

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20. 20.

    Physics

    Find the electrical power when 107 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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