AP Physics · Practice Sheet 4

1. 1.

   Physics

   A constant force of 45 N moves an object 30 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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2. 2.

   Physics

   Calculate the potential energy of a 2 kg object at a height of 42 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Physics

   A body moving at 14 m/s accelerates at 5 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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4. 4.

   Mathematics

   Find term number 7 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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5. 5.

   Mathematics

   If f(x) = 1x³ + 2x² + 6x, find f′(4).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Physics

   Find the electrical power when 54 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   Find the voltage across a 47 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Mathematics

   If f(x) = 4x³ + 3x² + 7x, find f′(5).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 18 and common difference 7, find term number 17.

   Formula:AP nth Term

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

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10. 10.

    Physics

    Find the voltage across a 33 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    For the quadratic 5x² + 1x − 9 = 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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12. 12.

    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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13. 13.

    Physics

    An object starts at 14 m/s and accelerates at 2 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 force of 145 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Mathematics

    Find the slope of the line through (5, 3) and (7, -6).

    Formula:Slope of a Line

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

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16. 16.

    Physics

    If 517 J of work is done in 11 s, find the power.

    Formula:Power

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

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17. 17.

    Physics

    A force of 704 N acts on an area of 50 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Mathematics

    Find the slope of the line through (3, 3) and (4, -4).

    Formula:Slope of a Line

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

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19. 19.

    Mathematics

    Find term number 4 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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20. 20.

    Mathematics

    Find the sum of the first 21 terms of an AP with first term 13 and common difference 2.

    Formula:AP Sum of n Terms

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

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