A-Level Physics · Practice Sheet 32

1. 1.

   Physics

   Find the force required to accelerate a 16 kg mass at 13 m/s².

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

   $F = ma$

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2. 2.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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3. 3.

   Physics

   An object starts at 1 m/s and accelerates at 5 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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4. 4.

   Physics

   Find the momentum of a 40 kg body moving at 11 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Physics

   Calculate the potential energy of a 47 kg object at a height of 34 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Physics

   Find the voltage across a 44 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Physics

   Find the electrical power when 189 V drives a current of 11 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Physics

   Find the momentum of a 49 kg body moving at 5 m/s.

   Formula:Linear Momentum

   $p = mv$

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9. 9.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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10. 10.

    Mathematics

    If f(x) = 5x³ + 5x² + 9x, find f′(3).

    Formula:Derivative of a Polynomial

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

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11. 11.

    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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12. 12.

    Mathematics

    Find the distance between the points (3, -3) and (8, -7).

    Formula:Distance Between Two Points

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

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13. 13.

    Physics

    An object starts at 20 m/s and accelerates at 8 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Physics

    A constant force of 52 N moves an object 19 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    Calculate the potential energy of a 23 kg object at a height of 27 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Mathematics

    Find the distance between the points (-8, -7) and (3, 4).

    Formula:Distance Between Two Points

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

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17. 17.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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18. 18.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 15 and common difference 1.

    Formula:AP Sum of n Terms

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

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19. 19.

    Physics

    Calculate the potential energy of a 10 kg object at a height of 8 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Physics

    Find the force required to accelerate a 20 kg mass at 9 m/s².

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

    $F = ma$

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