Ablock of ice with mass 5.50 kg is initially at rest on a frictionless, horizontal surface. a worker then applies a horizontal force f⃗ to it. as a result, the block moves along the x-axis such that its position as a function of time is given by x(t)

x ( t )  = F / 5.5  t²

Explanation:

acceleration dv / dt = F / 5.5

dv = F / 5.5  dt

integraring on both sides

v =  F / 5.5  t + c

when t = 0 , v = 0

c = 0

v =  F / 5.5  t

ds / dt  = F / 5.5  t

integrating on both sides

s = F / 5.5  t² + c₁

when t = 0 , s = 0

c = 0

so

x ( t )  = F / 5.5  t²

This is the required relation.