A 5.25-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t).

Explanation:

The upward force of F(t) is applied at the free end . Therefore the acceleration of  mass , suspended from rope can be calculated as

The displacement S = u t + 1/2 a t²

By substituting the values  S = 0 + 1/2 x F(t)/5.25 x t²

or  y(t) = 1/2 x F(t)/5.25 x t²

Here u is the initial velocity , because mass was at rest in the beginning , hence it is zero .

The acceleration a = force/mass = F(t)/5.25

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day