In this problem you are asked to design one-dimensional time-dependent force fields so that you can control the motion of particles. We will be considering time-dependent forces, F(t), which give rise to time-dependent accelerations on the particle's motion according to the expression
a(t)= F(t)/m​
where m is the particle's mass and function notation is used. You will need to answer two of three questions. Your resulting force fields will be piecewise functions, so you can write them as something like:
F(t)={1 0≤t<0. 67; -1 0. 67≤t≤1; 0 t>1
a. At t=0 a particle is at rest at x=0. Design a one-dimensional force field such that at t=1 the particle is at position x=2
b. At t=0 a particle is at rest at x=0. Design a one-dimensional force field such that at t=1 the particle is at position x=2 with velocity v=0 and sits there forever after.
c. At t=0 a particle is at rest at x=0. Design a one-dimensional force field such that at t=1 the particle is at position x=2 with velocity v=0, sitting at rest at x=0 for t>2.