A-Level Physics · Practice Sheet 44

1. 1.

   Mathematics

   Evaluate log base 10 of 1,000,000.

   Formula:Logarithm Evaluation

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

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2. 2.

   Physics

   A body moving at 12 m/s accelerates at 5 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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3. 3.

   Mathematics

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

   Formula:Slope of a Line

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

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4. 4.

   Physics

   A projectile is launched at 47 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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5. 5.

   Mathematics

   For the quadratic 5x² − 8x + 6 = 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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6. 6.

   Physics

   Calculate the potential energy of a 32 kg object at a height of 14 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 5 and common difference 4.

   Formula:AP Sum of n Terms

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

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8. 8.

   Mathematics

   Evaluate log base 10 of 100,000.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   A projectile is launched at 35 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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10. 10.

    Physics

    An object starts at 3 m/s and accelerates at 9 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    Find the kinetic energy of a 7 kg object moving at 16 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Physics

    Calculate the potential energy of a 42 kg object at a height of 45 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    A constant force of 54 N moves an object 49 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    If 2,840 J of work is done in 37 s, find the power.

    Formula:Power

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

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15. 15.

    Mathematics

    Find the distance between the points (-3, 1) and (2, 5).

    Formula:Distance Between Two Points

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

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16. 16.

    Physics

    Calculate the potential energy of a 16 kg object at a height of 11 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Mathematics

    For the quadratic 3x² − 3x + 7 = 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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18. 18.

    Physics

    Find the force required to accelerate a 41 kg mass at 6 m/s².

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

    $F = ma$

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19. 19.

    Physics

    Find the electrical power when 167 V drives a current of 20 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Physics

    Find the momentum of a 3 kg body moving at 15 m/s.

    Formula:Linear Momentum

    $p = mv$

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