A-Level Physics · Practice Sheet 45

1. 1.

   Mathematics

   Find the slope of the line through (1, 8) and (-8, -7).

   Formula:Slope of a Line

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

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2. 2.

   Physics

   A projectile is launched at 44 m/s at 45° 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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3. 3.

   Physics

   If 2,689 J of work is done in 22 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Find the distance between the points (-4, -1) and (-4, -7).

   Formula:Distance Between Two Points

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

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5. 5.

   Physics

   Calculate the potential energy of a 3 kg object at a height of 19 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Physics

   Find the momentum of a 12 kg body moving at 28 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Physics

   A projectile is launched at 31 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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8. 8.

   Physics

   Find the voltage across a 16 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   Find the momentum of a 25 kg body moving at 35 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    Find the voltage across a 27 Ω resistor carrying a current of 14 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Physics

    If 3,504 J of work is done in 46 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    A body moving at 15 m/s accelerates at 5 m/s² for 5 s. Find the distance travelled.

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

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

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13. 13.

    Physics

    Find the density of an object with mass 319 g and volume 32 cm³.

    Formula:Density

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

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14. 14.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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15. 15.

    Physics

    An object starts at 14 m/s and accelerates at 1 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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16. 16.

    Physics

    A body moving at 5 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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17. 17.

    Mathematics

    If f(x) = 2x³ + 1x² + 5x, find f′(4).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Physics

    A constant force of 84 N moves an object 40 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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20. 20.

    Physics

    If 1,006 J of work is done in 21 s, find the power.

    Formula:Power

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

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