A-Level Physics · Practice Sheet 37

1. 1.

   Physics

   Find the force required to accelerate a 45 kg mass at 3 m/s².

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

   $F = ma$

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2. 2.

   Physics

   Find the electrical power when 91 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Physics

   A constant force of 59 N moves an object 17 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Physics

   A body moving at 14 m/s accelerates at 5 m/s² for 6 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.

   Mathematics

   If f(x) = 3x³ + 5x² + 9x, find f′(3).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Physics

   An object starts at 11 m/s and accelerates at 5 m/s² for 11 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 3 and common difference 5.

   Formula:AP Sum of n Terms

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

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8. 8.

   Mathematics

   Evaluate ∫ from 0 to 5 of 5x^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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9. 9.

   Mathematics

   Find the slope of the line through (-4, 6) and (-3, 2).

   Formula:Slope of a Line

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

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10. 10.

    Physics

    An object starts at 11 m/s and accelerates at 9 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    Find the momentum of a 42 kg body moving at 34 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Physics

    A constant force of 32 N moves an object 42 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Physics

    Find the kinetic energy of a 10 kg object moving at 2 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    An object starts at 20 m/s and accelerates at 9 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Mathematics

    Find the slope of the line through (-2, -5) and (1, -2).

    Formula:Slope of a Line

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

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16. 16.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 7, find term number 26.

    Formula:AP nth Term

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

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18. 18.

    Physics

    Find the density of an object with mass 317 g and volume 28 cm³.

    Formula:Density

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 8, find term number 26.

    Formula:AP nth Term

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

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20. 20.

    Physics

    A projectile is launched at 38 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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