Answer:
Explanation:
Work: This can be defined as the product of force and distance. The unit of work is Joules (J). it can be expressed mathematically as
W = F×d
or
W = [tex]\int\limits^b_a {Fx} \, dx[/tex].................................. Equation 1
Where b = upper limit, a = lower limit, Fx = expression of force.
Given: a = 0 , b = 1.3 m, Fx = 4 + 15.7x - 1.5x²
Substituting these values into equation 1
W = [tex]\int\limits^a_b {(4 + 15.7x - 1.5x^{2} )dx} \,[/tex]
W = ᵇ[4x + 15.7x²/2-1.5x³/3 +C]ₐ
Work = upper limit - lower limit
Work = ᵃ[4x + 15.7x²/2 - 1.5x³/3 +C] - [4x + 15.7x²/2 + 1.5x³/3 +C]ᵇ............... Equation 2
Substituting the values of a and b into equation 2
Work = [4(1.3) + 15.7(1.3)²/2-1.5(1.3)³/3 + C] - [0 +C]
Work = [5.2 + 26.53 -3.29 + C] - C
Work = 28.44 J
Work done by the force = 28.44 J.
