Answer:
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
Explanation:
To find the variation of kinetic energy, let's use the work energy theorem
W = ΔK
∫ F .dx = K -K₀
If the body starts from rest K₀ = 0
∫ F dx cos θ = K
Since the force and displacement are in the same direction, the angle is zero, so the cosine is 1
we substitute and integrate
α ∫ x³ dx + β ∫ dx = K
α x⁴ / 4 + β x / 1 = K
we evaluate from the lower limit F = 0 to the upper limit F
α (x⁴ / 4 -0) + β (x -0) = K
K = αX⁴ / 4 + β x
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
in order to finish the calculation we must know the displacement