AP Physics · Practice Sheet 29

1. 1.

   Physics

   Find the force required to accelerate a 5 kg mass at 13 m/s².

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

   $F = ma$

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2. 2.

   Physics

   A projectile is launched at 26 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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3. 3.

   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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4. 4.

   Physics

   Find the voltage across a 15 Ω resistor carrying a current of 5 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Mathematics

   For the quadratic 2x² − 5x − 2 = 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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6. 6.

   Physics

   A force of 349 N acts on an area of 9 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Mathematics

   Find term number 6 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.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 1 and common ratio 2.

   Formula:GP Sum of n Terms

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

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9. 9.

   Mathematics

   For the quadratic 1x² − 1x − 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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10. 10.

    Physics

    An object starts at 11 m/s and accelerates at 5 m/s² for 2 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    A constant force of 15 N moves an object 11 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    For the quadratic 5x² − 2x − 6 = 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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13. 13.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 4, find term number 14.

    Formula:AP nth Term

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

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14. 14.

    Physics

    A projectile is launched at 17 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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15. 15.

    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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16. 16.

    Physics

    If 2,335 J of work is done in 36 s, find the power.

    Formula:Power

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

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17. 17.

    Physics

    Find the electrical power when 139 V drives a current of 12 A.

    Formula:Electrical Power

    $P = VI$

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18. 18.

    Physics

    A body moving at 8 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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19. 19.

    Mathematics

    Find the distance between the points (2, -5) and (-6, -1).

    Formula:Distance Between Two Points

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

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20. 20.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 12 and common difference 2.

    Formula:AP Sum of n Terms

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

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