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.