To understand the meaning and possible applications of the work-energy theorem.

in this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work-energy theorem. we will start with a special case: a particle of mass m moving in the x direction at constant acceleration a . during a certain interval of time, the particle accelerates from vinitial to vfinal , undergoing displacement s given by s=xfinal−xinitial

find the acceleration a of the particle.

    a = V final 2___v initial2

                      28

Explanation:

By definition for contant acceleration        a =   V final ___v initial

                                                                                      t

Furthermore the average speed is           V abg =  v initial +v final

                                                                                         2

Combine these relationships to eliminate t.               8 = Vabg t.

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