A) a block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. the spring projects the block along a frictionless horizontal surface, giving the block a speed v. the same spring projects a second block of mass 4m, giving it a speed 3v. what distance was the spring compressed in the second case?
b) initially a body moves in one direction and has kinetic energy k. then it moves in the opposite direction with three times its initial speed. what is the kinetic energy now?

a)

KE=1/2mv^2

F= -kx

KE= -kx

-kx= 1/2mv^2

when u quadruple the m, the x also quadruples. when the speed is multiplied by 3, since it is v^2, the x is multiplied by 3^2 , which is 9

so distance the spring compressed is x×4×9= 36x

b) using the KE formular too,

when the v is tripled, since formula is v^2, the resulting KE will be multiplied by 3^2, so KE now= 9K

would be false hope this out

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