A-Level Physics · Practice Sheet 29

1. 1.

   Physics

   If 4,731 J of work is done in 45 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   An object starts at 9 m/s and accelerates at 5 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Physics

   A body moving at 9 m/s accelerates at 7 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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4. 4.

   Physics

   Find the kinetic energy of a 4 kg object moving at 2 m/s.

   Formula:Kinetic Energy

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

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5. 5.

   Mathematics

   If f(x) = 1x³ + 5x² + 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

   A projectile is launched at 40 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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7. 7.

   Physics

   A constant force of 72 N moves an object 8 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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8. 8.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   A constant force of 57 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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10. 10.

    Mathematics

    Evaluate ∫ from 0 to 4 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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11. 11.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    If f(x) = 4x³ + 2x² + 3x, find f′(5).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 13 and common difference 9.

    Formula:AP Sum of n Terms

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

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14. 14.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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15. 15.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

    If f(x) = 3x³ + 2x² + 9x, find f′(2).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Physics

    A projectile is launched at 11 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.

    Physics

    A constant force of 103 N moves an object 12 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Physics

    Find the kinetic energy of a 15 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Mathematics

    Find the distance between the points (-4, 6) and (1, 2).

    Formula:Distance Between Two Points

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

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