AP Physics · Practice Sheet 48

1. 1.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 2, find term number 26.

   Formula:AP nth Term

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

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2. 2.

   Mathematics

   Find the sum of the first 7 terms of an AP with first term 19 and common difference 6.

   Formula:AP Sum of n Terms

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

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3. 3.

   Mathematics

   Find the slope of the line through (-6, -5) and (7, -6).

   Formula:Slope of a Line

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

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4. 4.

   Physics

   A body moving at 1 m/s accelerates at 8 m/s² for 7 s. Find the distance travelled.

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

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

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5. 5.

   Physics

   Find the electrical power when 226 V drives a current of 17 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Physics

   Find the density of an object with mass 185 g and volume 12 cm³.

   Formula:Density

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

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7. 7.

   Mathematics

   Find the slope of the line through (-2, -6) and (-4, 2).

   Formula:Slope of a Line

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

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8. 8.

   Physics

   A projectile is launched at 14 m/s at 60° 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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9. 9.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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10. 10.

    Physics

    Find the force required to accelerate a 43 kg mass at 13 m/s².

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

    $F = ma$

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11. 11.

    Physics

    A body moving at 4 m/s accelerates at 5 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

    For the quadratic 3x² − 6x + 5 = 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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13. 13.

    Mathematics

    If f(x) = 2x³ + 6x² + 3x, find f′(2).

    Formula:Derivative of a Polynomial

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

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14. 14.

    Physics

    Find the momentum of a 14 kg body moving at 2 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Physics

    A projectile is launched at 32 m/s at 60° 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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16. 16.

    Physics

    Find the momentum of a 24 kg body moving at 35 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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18. 18.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 19 and common difference 1.

    Formula:AP Sum of n Terms

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

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19. 19.

    Physics

    Find the force required to accelerate a 47 kg mass at 12 m/s².

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

    $F = ma$

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20. 20.

    Physics

    Find the kinetic energy of a 5 kg object moving at 3 m/s.

    Formula:Kinetic Energy

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

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