AP Physics · Practice Sheet 36

1. 1.

   Physics

   An object starts at 8 m/s and accelerates at 8 m/s² for 2 s. Find its final velocity.

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

   $v = u + at$

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2. 2.

   Physics

   A body moving at 2 m/s accelerates at 5 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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3. 3.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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4. 4.

   Mathematics

   For the quadratic 2x² + 9x − 8 = 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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5. 5.

   Mathematics

   Find the distance between the points (-8, 0) and (-7, 0).

   Formula:Distance Between Two Points

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

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6. 6.

   Physics

   An object starts at 12 m/s and accelerates at 9 m/s² for 4 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Physics

   A body moving at 6 m/s accelerates at 7 m/s² for 3 s. Find the distance travelled.

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

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

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8. 8.

   Physics

   Find the electrical power when 42 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Mathematics

   Find the slope of the line through (8, 6) and (-6, -4).

   Formula:Slope of a Line

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

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10. 10.

    Physics

    A body moving at 11 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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11. 11.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 7 and common difference 9.

    Formula:AP Sum of n Terms

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

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12. 12.

    Physics

    Calculate the potential energy of a 29 kg object at a height of 17 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    A constant force of 61 N moves an object 10 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    Find the voltage across a 34 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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16. 16.

    Physics

    Find the electrical power when 211 V drives a current of 6 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Physics

    Find the voltage across a 19 Ω resistor carrying a current of 9 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Mathematics

    Find term number 7 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term

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

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19. 19.

    Physics

    Find the momentum of a 50 kg body moving at 18 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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