AP Physics · Practice Sheet 35

1. 1.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   Calculate the potential energy of a 20 kg object at a height of 5 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 1, find term number 24.

   Formula:AP nth Term

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

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4. 4.

   Physics

   Find the force required to accelerate a 41 kg mass at 8 m/s².

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

   $F = ma$

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5. 5.

   Physics

   An object starts at 3 m/s and accelerates at 3 m/s² for 8 s. Find its final velocity.

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

   $v = u + at$

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6. 6.

   Physics

   A body moving at 12 m/s accelerates at 6 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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7. 7.

   Mathematics

   Find term number 7 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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8. 8.

   Physics

   An object starts at 16 m/s and accelerates at 2 m/s² for 6 s. Find its final velocity.

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

   $v = u + at$

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9. 9.

   Physics

   A body moving at 0 m/s accelerates at 2 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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10. 10.

    Physics

    A constant force of 117 N moves an object 33 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    An object starts at 13 m/s and accelerates at 5 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Physics

    Find the kinetic energy of a 20 kg object moving at 21 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Mathematics

    In an arithmetic progression with first term 8 and common difference 7, find term number 7.

    Formula:AP nth Term

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

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14. 14.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

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

    View formula →
15. 15.

    Mathematics

    For the quadratic 1x² + 5x − 7 = 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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16. 16.

    Physics

    Calculate the potential energy of a 21 kg object at a height of 34 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Physics

    A force of 806 N acts on an area of 33 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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19. 19.

    Physics

    Calculate the potential energy of a 26 kg object at a height of 23 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Physics

    If 2,978 J of work is done in 21 s, find the power.

    Formula:Power

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

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