A-Level Physics · Practice Sheet 39

1. 1.

   Physics

   A body moving at 4 m/s accelerates at 8 m/s² for 2 s. Find the distance travelled.

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

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

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2. 2.

   Mathematics

   Find the distance between the points (6, 7) and (4, -5).

   Formula:Distance Between Two Points

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

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3. 3.

   Physics

   Calculate the potential energy of a 46 kg object at a height of 21 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

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

   Formula:Distance Between Two Points

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

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5. 5.

   Mathematics

   Find term number 6 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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6. 6.

   Mathematics

   Evaluate log base 10 of 100,000.

   Formula:Logarithm Evaluation

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

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7. 7.

   Physics

   Calculate the potential energy of a 42 kg object at a height of 37 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Mathematics

   If f(x) = 5x³ + 1x² + 8x, find f′(5).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Physics

   A force of 532 N acts on an area of 16 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Physics

    An object starts at 15 m/s and accelerates at 10 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    A constant force of 174 N moves an object 22 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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13. 13.

    Physics

    An object starts at 7 m/s and accelerates at 1 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 3, find term number 10.

    Formula:AP nth Term

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

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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 3 of 1x^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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16. 16.

    Physics

    Find the momentum of a 32 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Physics

    A projectile is launched at 37 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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18. 18.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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19. 19.

    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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20. 20.

    Mathematics

    Find the slope of the line through (-6, 8) and (-1, -8).

    Formula:Slope of a Line

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

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