Engineering Entrance · Practice Sheet 12

1. 1.

   Physics

   Find the force required to accelerate a 16 kg mass at 11 m/s².

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

   $F = ma$

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2. 2.

   Physics

   Calculate the potential energy of a 43 kg object at a height of 27 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Physics

   A body moving at 6 m/s accelerates at 6 m/s² for 4 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

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

   Formula:Derivative of a Polynomial

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

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5. 5.

   Physics

   Find the voltage across a 21 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   Physics

   A constant force of 29 N moves an object 50 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Physics

   A force of 187 N acts on an area of 46 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Mathematics

   Evaluate ∫ from 0 to 3 of 3x^1 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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9. 9.

   Physics

   Find the voltage across a 17 Ω resistor carrying a current of 16 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Physics

    A body moving at 3 m/s accelerates at 7 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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11. 11.

    Physics

    A constant force of 21 N moves an object 26 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find the distance between the points (6, -4) and (-8, -8).

    Formula:Distance Between Two Points

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

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13. 13.

    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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14. 14.

    Physics

    Find the momentum of a 46 kg body moving at 24 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Physics

    A projectile is launched at 42 m/s at 60° 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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16. 16.

    Physics

    Find the electrical power when 42 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Physics

    An object starts at 5 m/s and accelerates at 9 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Physics

    Find the kinetic energy of a 2 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Physics

    A constant force of 77 N moves an object 31 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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20. 20.

    Physics

    A body moving at 11 m/s accelerates at 3 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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