Question

You push an object initially at rest across a frictionless floor

Answer 1

 t = t₀ / 2

Explanation:

In this exercise we must use Newton's second law

         F = m a

         a = F / m

now we can use kinematics

 as in object part of rest (v₀ = 0)

       v =a t₀

       t₀ = v / a

these results are with the first experiment

now repeat the experiment, but F = 2F₀

          a = 2F₀ / m = 2 a₀

         v = 2 a₀ t

         t = v / 2a₀

         t = t₀ / 2