AP Physics · Practice Sheet 25

1. 1.

   Physics

   Calculate the potential energy of a 9 kg object at a height of 47 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Physics

   Find the kinetic energy of a 11 kg object moving at 18 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   A projectile is launched at 18 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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4. 4.

   Physics

   A body moving at 5 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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5. 5.

   Mathematics

   Evaluate ∫ from 0 to 5 of 2x^2 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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6. 6.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 8 and common difference 8.

   Formula:AP Sum of n Terms

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 3, find term number 7.

   Formula:AP nth Term

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

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8. 8.

   Physics

   A constant force of 175 N moves an object 43 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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9. 9.

   Physics

   Find the density of an object with mass 356 g and volume 20 cm³.

   Formula:Density

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

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10. 10.

    Mathematics

    For the quadratic 3x² + 0x − 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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11. 11.

    Physics

    Calculate the potential energy of a 30 kg object at a height of 23 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Mathematics

    Find the sum of the first 15 terms of an AP with first term 10 and common difference 7.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    If 4,529 J of work is done in 41 s, find the power.

    Formula:Power

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

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14. 14.

    Physics

    A constant force of 132 N moves an object 20 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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16. 16.

    Physics

    Find the electrical power when 197 V drives a current of 5 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Physics

    If 4,840 J of work is done in 26 s, find the power.

    Formula:Power

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

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18. 18.

    Mathematics

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

    Formula:GP nth Term

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

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19. 19.

    Physics

    If 1,363 J of work is done in 11 s, find the power.

    Formula:Power

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

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20. 20.

    Mathematics

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

    Formula:Distance Between Two Points

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

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