Find the displacement of a particle if v(t) = t⁷; [-3, 0]. A) 819.125 B) -312.428 C) 6,561 D) -820.125 E) -2,187

Question

Quizplus · Accepted Answer

The displacement of the particle is given by the integral of the velocity function. Integrating v(t), we get the displacement function as s(t) = (1/2) t^2 ⁷ + C, where C is the constant of integration. We can now use the given boundary condition to find C: s(-3) = (1/2) (-3)^2 ⁷ + C = 0 C = (1/2) (9) ⁷ = 4.5 ⁷ Therefore, the displacement function is s(t) = (1/2) t^2 ⁷ + 4.5 ⁷ The displacement of the particle from t = -3 to t = 0 is given by s(0) - s(-3) = [(1/2) (0)^2 - (1/2) (-3)^2] ⁷ = -4.5 ⁷ So, the best choice is D) -820.125.

Find the Displacement of a Particle If V(t) = T7;

Find the Displacement of a Particle If V(t) = T⁷;