Answer:
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
Explanation:
To calculate the kinetic energy variation, we can utilize the work-energy theorem.
W = ΔK
∫ F .dx = K - K₀
If the object starts from rest, then K₀ = 0.
So, ∫ F dx cos θ = K.
As the force and displacement directions align, the angle is zero, and hence the cosine is 1.
Now we can substitute and perform integration:
α ∫ x³ dx + β ∫ dx = K.
Thus, α x⁴ / 4 + β x = K.
Next, we evaluate from the limits F = 0 to F:
α (x⁴ / 4 - 0) + β (x - 0) = K.
Consequently, K = αX⁴ / 4 + β x.
This results in K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x.
To finalize the computation, we need to ascertain the displacement.
