This is a wild guess here.
I'm thinking you believe ListPlot means plot this list of functions.
I believe Mathematica thinks ListPlot means plot this list of data points.
http://reference.wolfram.com/mathema...stPlot&lang=en
I do not believe ListPlot creates lists of points for you.
Perhaps try
Manipulate[Plot[{
0.02 t^2,...
and see what you get.
Plot[{a list of functions}
should plot that list of functions on top of each other.
OR
Temporarily throw away your Manipulate and just see what
ListPlot[{
0.02 t^2,...
does for a specific value of t. If that doesn't work then you have narrowed down your problem.