A-Level Physics · Practice Sheet 4

1. 1.

   Physics

   A projectile is launched at 22 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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2. 2.

   Physics

   A constant force of 78 N moves an object 9 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Mathematics

   If f(x) = 3x³ + 5x² + 6x, find f′(1).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Physics

   A body moving at 12 m/s accelerates at 8 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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5. 5.

   Mathematics

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

   Formula:Distance Between Two Points

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

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6. 6.

   Physics

   Find the momentum of a 46 kg body moving at 10 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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8. 8.

   Physics

   Find the force required to accelerate a 38 kg mass at 8 m/s².

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

   $F = ma$

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9. 9.

   Physics

   If 3,989 J of work is done in 46 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

    Find the voltage across a 10 Ω resistor carrying a current of 17 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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12. 12.

    Mathematics

    Find the slope of the line through (-5, 1) and (-6, -8).

    Formula:Slope of a Line

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

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13. 13.

    Mathematics

    In an arithmetic progression with first term 5 and common difference 10, find term number 21.

    Formula:AP nth Term

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

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14. 14.

    Physics

    A projectile is launched at 41 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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15. 15.

    Physics

    Find the kinetic energy of a 17 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Physics

    Find the force required to accelerate a 7 kg mass at 17 m/s².

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

    $F = ma$

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17. 17.

    Physics

    Calculate the potential energy of a 14 kg object at a height of 38 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Physics

    If 2,941 J of work is done in 35 s, find the power.

    Formula:Power

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

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19. 19.

    Physics

    Find the electrical power when 2 V drives a current of 1 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Physics

    Find the kinetic energy of a 20 kg object moving at 26 m/s.

    Formula:Kinetic Energy

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

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